{"id":"https://openalex.org/W2963400112","doi":"https://doi.org/10.1142/s1793830916500531","title":"Two coloring problems on matrix graphs","display_name":"Two coloring problems on matrix graphs","publication_year":2016,"publication_date":"2016-06-30","ids":{"openalex":"https://openalex.org/W2963400112","doi":"https://doi.org/10.1142/s1793830916500531","mag":"2963400112"},"language":"en","primary_location":{"id":"doi:10.1142/s1793830916500531","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s1793830916500531","pdf_url":null,"source":{"id":"https://openalex.org/S178434951","display_name":"Discrete Mathematics Algorithms and Applications","issn_l":"1793-8309","issn":["1793-8309","1793-8317"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete Mathematics, Algorithms and Applications","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/A5026486739","display_name":"Zhe Han","orcid":null},"institutions":[{"id":"https://openalex.org/I201448701","display_name":"University of Washington","ror":"https://ror.org/00cvxb145","country_code":"US","type":"education","lineage":["https://openalex.org/I201448701"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Zhe Han","raw_affiliation_strings":["Department of Computer Science and Engineering, University of Washington, Seattle, WA 98195, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science and Engineering, University of Washington, Seattle, WA 98195, USA","institution_ids":["https://openalex.org/I201448701"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101950647","display_name":"Mei Lu","orcid":"https://orcid.org/0000-0001-9461-0640"},"institutions":[{"id":"https://openalex.org/I99065089","display_name":"Tsinghua University","ror":"https://ror.org/03cve4549","country_code":"CN","type":"education","lineage":["https://openalex.org/I99065089"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Mei Lu","raw_affiliation_strings":["Department of Mathematical Sciences, Tsinghua University, Beijing 100084, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, Tsinghua University, Beijing 100084, P. R. China","institution_ids":["https://openalex.org/I99065089"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.24814854,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"08","issue":"03","first_page":"1650053","last_page":"1650053"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10849","display_name":"Finite Group Theory Research","score":0.9968000054359436,"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/T11130","display_name":"Coding theory and cryptography","score":0.9955999851226807,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/combinatorics","display_name":"Combinatorics","score":0.6994322538375854},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6424891948699951},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.5431813597679138},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.4788770079612732},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.43948444724082947},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4097203016281128},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.37848198413848877}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6994322538375854},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6424891948699951},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.5431813597679138},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.4788770079612732},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.43948444724082947},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4097203016281128},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.37848198413848877},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s1793830916500531","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s1793830916500531","pdf_url":null,"source":{"id":"https://openalex.org/S178434951","display_name":"Discrete Mathematics Algorithms and Applications","issn_l":"1793-8309","issn":["1793-8309","1793-8317"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete Mathematics, Algorithms and Applications","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W1596146664","https://openalex.org/W1989388823","https://openalex.org/W2005781890","https://openalex.org/W2021640907","https://openalex.org/W2029496510","https://openalex.org/W2055322834","https://openalex.org/W2095547380","https://openalex.org/W2100597435","https://openalex.org/W2113113620","https://openalex.org/W2139416652","https://openalex.org/W2964014596"],"related_works":["https://openalex.org/W2152992791","https://openalex.org/W2112835755","https://openalex.org/W2349674371","https://openalex.org/W2361403716","https://openalex.org/W2904061867","https://openalex.org/W4289115725","https://openalex.org/W2967798957","https://openalex.org/W3144644423","https://openalex.org/W2024384195","https://openalex.org/W2514587231"],"abstract_inverted_index":{"In":[0,137],"this":[1,138],"paper,":[2,139],"we":[3,63,140],"propose":[4],"a":[5,28,108],"new":[6],"family":[7],"of":[8,21,55,68,91,132,134,145],"graphs,":[9,11],"matrix":[10,98],"whose":[12],"vertex":[13],"set":[14,20],"[Formula:":[15,23,31,38,42,59,80,84,112,117,146,157],"see":[16,24,32,39,43,60,81,85,113,118,147,158],"text]":[17,25,33,40,82,114,148],"is":[18,58],"the":[19,53,88,96,121,130,142],"all":[22],"matrices":[26,48],"over":[27],"finite":[29],"field":[30],"for":[34],"any":[35,46],"positive":[36],"integers":[37],"and":[41,71,149,153],"text].":[44,61,159],"And":[45],"two":[47,74,103,125],"share":[49],"an":[50],"edge":[51],"if":[52],"rank":[54],"their":[56],"difference":[57],"Next,":[62],"give":[64,150],"some":[65,151],"basic":[66],"properties":[67],"such":[69],"graphs":[70],"also":[72],"consider":[73],"coloring":[75],"problems":[76,126],"on":[77,156],"them.":[78],"Let":[79],"(resp.,":[83,115],"text])":[86,119],"denote":[87],"minimum":[89],"number":[90],"colors":[92],"necessary":[93],"to":[94],"color":[95],"above":[97],"graph":[99],"so":[100],"that":[101,105],"no":[102],"vertices":[104],"are":[106],"at":[107,110],"distance":[109],"most":[111],"exactly":[116],"get":[120],"same":[122],"color.":[123],"These":[124],"were":[127],"proposed":[128],"in":[129],"study":[131],"scalability":[133],"optical":[135],"networks.":[136],"determine":[141],"exact":[143],"value":[144],"upper":[152],"lower":[154],"bounds":[155]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}