{"id":"https://openalex.org/W3167034228","doi":"https://doi.org/10.1137/19m1299128","title":"From Independent Sets and Vertex Colorings to Isotropic Spaces and Isotropic Decompositions: Another Bridge between Graphs and Alternating Matrix Spaces","display_name":"From Independent Sets and Vertex Colorings to Isotropic Spaces and Isotropic Decompositions: Another Bridge between Graphs and Alternating Matrix Spaces","publication_year":2021,"publication_date":"2021-01-01","ids":{"openalex":"https://openalex.org/W3167034228","doi":"https://doi.org/10.1137/19m1299128","mag":"3167034228"},"language":"en","primary_location":{"id":"doi:10.1137/19m1299128","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m1299128","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5082638698","display_name":"Xiaohui Bei","orcid":"https://orcid.org/0000-0002-0870-5019"},"institutions":[{"id":"https://openalex.org/I114017466","display_name":"University of Technology Sydney","ror":"https://ror.org/03f0f6041","country_code":"AU","type":"education","lineage":["https://openalex.org/I114017466"]},{"id":"https://openalex.org/I172675005","display_name":"Nanyang Technological University","ror":"https://ror.org/02e7b5302","country_code":"SG","type":"education","lineage":["https://openalex.org/I172675005"]},{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210090176","display_name":"Institute of Computing Technology","ror":"https://ror.org/0090r4d87","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210090176"]},{"id":"https://openalex.org/I4210096034","display_name":"Centre for Quantum Computation and Communication Technology","ror":"https://ror.org/00rnbty21","country_code":"AU","type":"facility","lineage":["https://openalex.org/I1337719021","https://openalex.org/I165143802","https://openalex.org/I2801453606","https://openalex.org/I4210096034","https://openalex.org/I4210132349"]},{"id":"https://openalex.org/I4210128818","display_name":"Institute of Software","ror":"https://ror.org/033dfsn42","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210128818"]},{"id":"https://openalex.org/I4210165038","display_name":"University of Chinese Academy of Sciences","ror":"https://ror.org/05qbk4x57","country_code":"CN","type":"education","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210165038"]}],"countries":["AU","CN","SG"],"is_corresponding":false,"raw_author_name":"Xiaohui Bei","raw_affiliation_strings":["Centre for Quantum Software and Information, University of Technology Sydney, Australia","School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore","Institute of Computing Technology, Chinese Academy of Sciences and University of Chinese Academy of Sciences, Beijing, China","State Key Laboratory of Computer Science, Institute of Software, Chinese Academy of Sciences, Beijing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Centre for Quantum Software and Information, University of Technology Sydney, Australia","institution_ids":["https://openalex.org/I4210096034","https://openalex.org/I114017466"]},{"raw_affiliation_string":"School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore","institution_ids":["https://openalex.org/I172675005"]},{"raw_affiliation_string":"Institute of Computing Technology, Chinese Academy of Sciences and University of Chinese Academy of Sciences, Beijing, China","institution_ids":["https://openalex.org/I4210090176","https://openalex.org/I4210165038"]},{"raw_affiliation_string":"State Key Laboratory of Computer Science, Institute of Software, Chinese Academy of Sciences, Beijing, China","institution_ids":["https://openalex.org/I4210128818","https://openalex.org/I19820366"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5003095336","display_name":"Shiteng Chen","orcid":"https://orcid.org/0000-0002-0658-628X"},"institutions":[{"id":"https://openalex.org/I114017466","display_name":"University of Technology Sydney","ror":"https://ror.org/03f0f6041","country_code":"AU","type":"education","lineage":["https://openalex.org/I114017466"]},{"id":"https://openalex.org/I172675005","display_name":"Nanyang Technological University","ror":"https://ror.org/02e7b5302","country_code":"SG","type":"education","lineage":["https://openalex.org/I172675005"]},{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210090176","display_name":"Institute of Computing Technology","ror":"https://ror.org/0090r4d87","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210090176"]},{"id":"https://openalex.org/I4210096034","display_name":"Centre for Quantum Computation and Communication Technology","ror":"https://ror.org/00rnbty21","country_code":"AU","type":"facility","lineage":["https://openalex.org/I1337719021","https://openalex.org/I165143802","https://openalex.org/I2801453606","https://openalex.org/I4210096034","https://openalex.org/I4210132349"]},{"id":"https://openalex.org/I4210128818","display_name":"Institute of Software","ror":"https://ror.org/033dfsn42","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210128818"]},{"id":"https://openalex.org/I4210165038","display_name":"University of Chinese Academy of Sciences","ror":"https://ror.org/05qbk4x57","country_code":"CN","type":"education","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210165038"]}],"countries":["AU","CN","SG"],"is_corresponding":false,"raw_author_name":"Shiteng Chen","raw_affiliation_strings":["Institute of Computing Technology, Chinese Academy of Sciences and University of Chinese Academy of Sciences, Beijing, China","Centre for Quantum Software and Information, University of Technology Sydney, Australia","School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore","State Key Laboratory of Computer Science, Institute of Software, Chinese Academy of Sciences, Beijing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Computing Technology, Chinese Academy of Sciences and University of Chinese Academy of Sciences, Beijing, China","institution_ids":["https://openalex.org/I4210090176","https://openalex.org/I4210165038"]},{"raw_affiliation_string":"Centre for Quantum Software and Information, University of Technology Sydney, Australia","institution_ids":["https://openalex.org/I4210096034","https://openalex.org/I114017466"]},{"raw_affiliation_string":"School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore","institution_ids":["https://openalex.org/I172675005"]},{"raw_affiliation_string":"State Key Laboratory of Computer Science, Institute of Software, Chinese Academy of Sciences, Beijing, China","institution_ids":["https://openalex.org/I4210128818","https://openalex.org/I19820366"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5081435269","display_name":"Ji Guan","orcid":"https://orcid.org/0000-0002-3490-0029"},"institutions":[{"id":"https://openalex.org/I114017466","display_name":"University of Technology Sydney","ror":"https://ror.org/03f0f6041","country_code":"AU","type":"education","lineage":["https://openalex.org/I114017466"]},{"id":"https://openalex.org/I172675005","display_name":"Nanyang Technological University","ror":"https://ror.org/02e7b5302","country_code":"SG","type":"education","lineage":["https://openalex.org/I172675005"]},{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210090176","display_name":"Institute of Computing Technology","ror":"https://ror.org/0090r4d87","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210090176"]},{"id":"https://openalex.org/I4210096034","display_name":"Centre for Quantum Computation and Communication Technology","ror":"https://ror.org/00rnbty21","country_code":"AU","type":"facility","lineage":["https://openalex.org/I1337719021","https://openalex.org/I165143802","https://openalex.org/I2801453606","https://openalex.org/I4210096034","https://openalex.org/I4210132349"]},{"id":"https://openalex.org/I4210128818","display_name":"Institute of Software","ror":"https://ror.org/033dfsn42","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210128818"]},{"id":"https://openalex.org/I4210165038","display_name":"University of Chinese Academy of Sciences","ror":"https://ror.org/05qbk4x57","country_code":"CN","type":"education","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210165038"]}],"countries":["AU","CN","SG"],"is_corresponding":false,"raw_author_name":"Ji Guan","raw_affiliation_strings":["Institute of Computing Technology, Chinese Academy of Sciences and University of Chinese Academy of Sciences, Beijing, China","Centre for Quantum Software and Information, University of Technology Sydney, Australia","School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore","State Key Laboratory of Computer Science, Institute of Software, Chinese Academy of Sciences, Beijing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Computing Technology, Chinese Academy of Sciences and University of Chinese Academy of Sciences, Beijing, China","institution_ids":["https://openalex.org/I4210090176","https://openalex.org/I4210165038"]},{"raw_affiliation_string":"Centre for Quantum Software and Information, University of Technology Sydney, Australia","institution_ids":["https://openalex.org/I4210096034","https://openalex.org/I114017466"]},{"raw_affiliation_string":"School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore","institution_ids":["https://openalex.org/I172675005"]},{"raw_affiliation_string":"State Key Laboratory of Computer Science, Institute of Software, Chinese Academy of Sciences, Beijing, China","institution_ids":["https://openalex.org/I4210128818","https://openalex.org/I19820366"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5054605479","display_name":"Youming Qiao","orcid":"https://orcid.org/0000-0003-4334-1449"},"institutions":[{"id":"https://openalex.org/I114017466","display_name":"University of Technology Sydney","ror":"https://ror.org/03f0f6041","country_code":"AU","type":"education","lineage":["https://openalex.org/I114017466"]},{"id":"https://openalex.org/I172675005","display_name":"Nanyang Technological University","ror":"https://ror.org/02e7b5302","country_code":"SG","type":"education","lineage":["https://openalex.org/I172675005"]},{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210090176","display_name":"Institute of Computing Technology","ror":"https://ror.org/0090r4d87","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210090176"]},{"id":"https://openalex.org/I4210096034","display_name":"Centre for Quantum Computation and Communication Technology","ror":"https://ror.org/00rnbty21","country_code":"AU","type":"facility","lineage":["https://openalex.org/I1337719021","https://openalex.org/I165143802","https://openalex.org/I2801453606","https://openalex.org/I4210096034","https://openalex.org/I4210132349"]},{"id":"https://openalex.org/I4210128818","display_name":"Institute of Software","ror":"https://ror.org/033dfsn42","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210128818"]},{"id":"https://openalex.org/I4210165038","display_name":"University of Chinese Academy of Sciences","ror":"https://ror.org/05qbk4x57","country_code":"CN","type":"education","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210165038"]}],"countries":["AU","CN","SG"],"is_corresponding":false,"raw_author_name":"Youming Qiao","raw_affiliation_strings":["School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore","State Key Laboratory of Computer Science, Institute of Software, Chinese Academy of Sciences, Beijing, China","Centre for Quantum Software and Information, University of Technology Sydney, Australia","Institute of Computing Technology, Chinese Academy of Sciences and University of Chinese Academy of Sciences, Beijing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore","institution_ids":["https://openalex.org/I172675005"]},{"raw_affiliation_string":"State Key Laboratory of Computer Science, Institute of Software, Chinese Academy of Sciences, Beijing, China","institution_ids":["https://openalex.org/I4210128818","https://openalex.org/I19820366"]},{"raw_affiliation_string":"Centre for Quantum Software and Information, University of Technology Sydney, Australia","institution_ids":["https://openalex.org/I4210096034","https://openalex.org/I114017466"]},{"raw_affiliation_string":"Institute of Computing Technology, Chinese Academy of Sciences and University of Chinese Academy of Sciences, Beijing, China","institution_ids":["https://openalex.org/I4210090176","https://openalex.org/I4210165038"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5000241520","display_name":"Xiaoming Sun","orcid":"https://orcid.org/0000-0002-0281-1670"},"institutions":[{"id":"https://openalex.org/I114017466","display_name":"University of Technology Sydney","ror":"https://ror.org/03f0f6041","country_code":"AU","type":"education","lineage":["https://openalex.org/I114017466"]},{"id":"https://openalex.org/I172675005","display_name":"Nanyang Technological University","ror":"https://ror.org/02e7b5302","country_code":"SG","type":"education","lineage":["https://openalex.org/I172675005"]},{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210090176","display_name":"Institute of Computing Technology","ror":"https://ror.org/0090r4d87","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210090176"]},{"id":"https://openalex.org/I4210096034","display_name":"Centre for Quantum Computation and Communication Technology","ror":"https://ror.org/00rnbty21","country_code":"AU","type":"facility","lineage":["https://openalex.org/I1337719021","https://openalex.org/I165143802","https://openalex.org/I2801453606","https://openalex.org/I4210096034","https://openalex.org/I4210132349"]},{"id":"https://openalex.org/I4210128818","display_name":"Institute of Software","ror":"https://ror.org/033dfsn42","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210128818"]},{"id":"https://openalex.org/I4210165038","display_name":"University of Chinese Academy of Sciences","ror":"https://ror.org/05qbk4x57","country_code":"CN","type":"education","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210165038"]}],"countries":["AU","CN","SG"],"is_corresponding":false,"raw_author_name":"Xiaoming Sun","raw_affiliation_strings":["State Key Laboratory of Computer Science, Institute of Software, Chinese Academy of Sciences, Beijing, China","Institute of Computing Technology, Chinese Academy of Sciences and University of Chinese Academy of Sciences, Beijing, China","Centre for Quantum Software and Information, University of Technology Sydney, Australia","School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"State Key Laboratory of Computer Science, Institute of Software, Chinese Academy of Sciences, Beijing, China","institution_ids":["https://openalex.org/I4210128818","https://openalex.org/I19820366"]},{"raw_affiliation_string":"Institute of Computing Technology, Chinese Academy of Sciences and University of Chinese Academy of Sciences, Beijing, China","institution_ids":["https://openalex.org/I4210090176","https://openalex.org/I4210165038"]},{"raw_affiliation_string":"Centre for Quantum Software and Information, University of Technology Sydney, Australia","institution_ids":["https://openalex.org/I4210096034","https://openalex.org/I114017466"]},{"raw_affiliation_string":"School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore","institution_ids":["https://openalex.org/I172675005"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":5,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.6089,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.71967419,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"50","issue":"3","first_page":"924","last_page":"971"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9994000196456909,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8089903593063354},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6694061756134033},{"id":"https://openalex.org/keywords/maximal-independent-set","display_name":"Maximal independent set","score":0.5919070839881897},{"id":"https://openalex.org/keywords/bipartite-graph","display_name":"Bipartite graph","score":0.5319238901138306},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.5079060196876526},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4876081049442291},{"id":"https://openalex.org/keywords/chordal-graph","display_name":"Chordal graph","score":0.3645859956741333},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.21632790565490723},{"id":"https://openalex.org/keywords/1-planar-graph","display_name":"1-planar graph","score":0.1561330258846283}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8089903593063354},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6694061756134033},{"id":"https://openalex.org/C18359143","wikidata":"https://www.wikidata.org/wiki/Q7888149","display_name":"Maximal independent set","level":5,"score":0.5919070839881897},{"id":"https://openalex.org/C197657726","wikidata":"https://www.wikidata.org/wiki/Q174733","display_name":"Bipartite graph","level":3,"score":0.5319238901138306},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.5079060196876526},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4876081049442291},{"id":"https://openalex.org/C160446614","wikidata":"https://www.wikidata.org/wiki/Q1322892","display_name":"Chordal graph","level":3,"score":0.3645859956741333},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.21632790565490723},{"id":"https://openalex.org/C102192266","wikidata":"https://www.wikidata.org/wiki/Q4545823","display_name":"1-planar graph","level":4,"score":0.1561330258846283}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/19m1299128","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m1299128","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Computing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G28403681","display_name":null,"funder_award_id":"XDB28000000","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3277130425","display_name":null,"funder_award_id":"DECRA DE150100720","funder_id":"https://openalex.org/F4320334704","funder_display_name":"Australian Research Council"},{"id":"https://openalex.org/G4894050043","display_name":null,"funder_award_id":"61832003","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5554334370","display_name":null,"funder_award_id":"61702489","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5956995831","display_name":null,"funder_award_id":"QYZDJ-SSW-SYS003","funder_id":"https://openalex.org/F4320321133","funder_display_name":"Chinese Academy of Sciences"},{"id":"https://openalex.org/G75260446","display_name":null,"funder_award_id":"61761136014","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8332624565","display_name":"\u91cf\u5b50\u7a0b\u5e8f\u8bbe\u8ba1\u7684\u7406\u8bba\u57fa\u7840","funder_award_id":"61832015","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8777218368","display_name":null,"funder_award_id":"XDB28000000","funder_id":"https://openalex.org/F4320321133","funder_display_name":"Chinese Academy of Sciences"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320321133","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35"},{"id":"https://openalex.org/F4320327721","display_name":"K. C. Wong Education Foundation","ror":null},{"id":"https://openalex.org/F4320334704","display_name":"Australian Research Council","ror":"https://ror.org/05mmh0f86"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":77,"referenced_works":["https://openalex.org/W1666394328","https://openalex.org/W1781417686","https://openalex.org/W1905051757","https://openalex.org/W1964504124","https://openalex.org/W1966991151","https://openalex.org/W1967069465","https://openalex.org/W1967971164","https://openalex.org/W1969557621","https://openalex.org/W1977706735","https://openalex.org/W1979412257","https://openalex.org/W1985012506","https://openalex.org/W1985061810","https://openalex.org/W1985413993","https://openalex.org/W1987631685","https://openalex.org/W1988642505","https://openalex.org/W1990283121","https://openalex.org/W1991813962","https://openalex.org/W2006114752","https://openalex.org/W2007200873","https://openalex.org/W2007940874","https://openalex.org/W2009819193","https://openalex.org/W2011170321","https://openalex.org/W2013568176","https://openalex.org/W2015332959","https://openalex.org/W2015540166","https://openalex.org/W2015555828","https://openalex.org/W2026036943","https://openalex.org/W2031385132","https://openalex.org/W2034592750","https://openalex.org/W2055472648","https://openalex.org/W2055940287","https://openalex.org/W2057753596","https://openalex.org/W2063292248","https://openalex.org/W2064232744","https://openalex.org/W2068243918","https://openalex.org/W2072903686","https://openalex.org/W2073034188","https://openalex.org/W2073595705","https://openalex.org/W2074359677","https://openalex.org/W2076795871","https://openalex.org/W2078637176","https://openalex.org/W2079460463","https://openalex.org/W2079722433","https://openalex.org/W2080132708","https://openalex.org/W2082002555","https://openalex.org/W2085236919","https://openalex.org/W2086416553","https://openalex.org/W2087392392","https://openalex.org/W2089417393","https://openalex.org/W2093776691","https://openalex.org/W2094752431","https://openalex.org/W2112046594","https://openalex.org/W2122639972","https://openalex.org/W2124240997","https://openalex.org/W2160030737","https://openalex.org/W2200115418","https://openalex.org/W2326898909","https://openalex.org/W2329328639","https://openalex.org/W2396964413","https://openalex.org/W2399980850","https://openalex.org/W2409645877","https://openalex.org/W2610479830","https://openalex.org/W2610680804","https://openalex.org/W2610729871","https://openalex.org/W2763302490","https://openalex.org/W2787337287","https://openalex.org/W2942921829","https://openalex.org/W2962732920","https://openalex.org/W2962745033","https://openalex.org/W2962789909","https://openalex.org/W2962817959","https://openalex.org/W2963597942","https://openalex.org/W2963989485","https://openalex.org/W3098943549","https://openalex.org/W3103419625","https://openalex.org/W3104123394","https://openalex.org/W3160627641"],"related_works":["https://openalex.org/W1555816812","https://openalex.org/W1966320878","https://openalex.org/W4283803822","https://openalex.org/W2029336174","https://openalex.org/W1994963913","https://openalex.org/W2963009577","https://openalex.org/W2063494850","https://openalex.org/W2788975631","https://openalex.org/W2903402681","https://openalex.org/W3199257895"],"abstract_inverted_index":{"In":[0,71],"the":[1,14,39,43,76,88,122,128,134,140,173,186,196,203,206,210,244],"1970s,":[2],"Lov\u00e1sz":[3],"built":[4],"a":[5,35,238],"bridge":[6,80],"between":[7,28,81,205,219],"graphs":[8,30,82],"and":[9,31,61,83,93,106,115,127,139,151,156,165,181,202,209,222,232,235],"alternating":[10,84,100],"matrix":[11,32,85,101],"spaces,":[12,86],"in":[13,38,87,99,112,243],"context":[15,89,245],"of":[16,20,42,52,90,198,240,246],"perfect":[17],"matchings":[18],"[Proceedings":[19],"FCT,":[21],"1979,":[22],"pp.":[23,55,69],"565--574].":[24],"A":[25],"similar":[26],"connection":[27],"bipartite":[29,179],"spaces":[33,102,105,164],"plays":[34],"key":[36],"role":[37],"recent":[40],"resolutions":[41],"noncommutative":[44],"rank":[45],"problem":[46,126,131,138,177],"[A.":[47],"Garg":[48],"et":[49],"al.,":[50],"Proceedings":[51],"FOCS,":[53],"2016,":[54],"109--117;":[56],"G.":[57],"Ivanyos,":[58],"Y.":[59],"Qiao,":[60],"K.":[62],"V.":[63],"Subrahmanyam,":[64],"Comput.":[65],"Complexity,":[66],"26":[67],"(2017),":[68],"717--763].":[70],"this":[72],"paper,":[73],"we":[74,146,236,251],"lay":[75],"foundation":[77],"for":[78,162,178,185,256],"another":[79],"independent":[91,124,154,175,200],"sets":[92,155],"vertex":[94,129,157],"colorings.":[95],"The":[96],"corresponding":[97],"structures":[98,111,242],"are":[103],"isotropic":[104,107,136,141,163],"decompositions,":[108],"both":[109],"useful":[110],"group":[113,230],"theory":[114,221,231],"manifold":[116,233],"theory.":[117,249],"We":[118],"first":[119],"show":[120,147],"that":[121,148],"maximum":[123,135,174,207],"set":[125,176],"$c$-coloring":[130],"reduce":[132],"to":[133,216,229],"space":[137],"$c$-decomposition":[142],"problem,":[143],"respectively.":[144],"Next,":[145],"several":[149,253],"topics":[150],"results":[152,225],"about":[153],"colorings":[158],"have":[159,226],"natural":[160],"correspondences":[161],"decompositions.":[166],"These":[167,213],"include":[168],"algorithmic":[169],"problems,":[170],"such":[171,194],"as":[172,189,191,195],"graphs,":[180],"exact":[182],"exponential-time":[183],"algorithms":[184],"chromatic":[187,211],"number,":[188],"well":[190],"mathematical":[192],"questions,":[193],"number":[197],"maximal":[199],"sets,":[201],"relation":[204],"degree":[208],"number.":[212],"connections":[214],"lead":[215],"new":[217],"interactions":[218],"graph":[220],"algebra.":[223],"Some":[224],"concrete":[227],"applications":[228],"theory,":[234],"initiate":[237],"variant":[239],"these":[241],"quantum":[247],"information":[248],"Finally,":[250],"propose":[252],"open":[254],"questions":[255],"further":[257],"exploration.":[258]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2020,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
