{"id":"https://openalex.org/W2038607360","doi":"https://doi.org/10.1007/s10878-011-9440-0","title":"Approximate min-max relations on plane graphs","display_name":"Approximate min-max relations on plane graphs","publication_year":2011,"publication_date":"2011-12-16","ids":{"openalex":"https://openalex.org/W2038607360","doi":"https://doi.org/10.1007/s10878-011-9440-0","mag":"2038607360"},"language":"en","primary_location":{"id":"doi:10.1007/s10878-011-9440-0","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10878-011-9440-0","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10878-011-9440-0.pdf","source":{"id":"https://openalex.org/S107925523","display_name":"Journal of Combinatorial Optimization","issn_l":"1382-6905","issn":["1382-6905","1573-2886"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by-nc","license_id":"https://openalex.org/licenses/cc-by-nc","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Combinatorial Optimization","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s10878-011-9440-0.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5007960147","display_name":"Jie Ma","orcid":"https://orcid.org/0000-0002-0095-255X"},"institutions":[{"id":"https://openalex.org/I130701444","display_name":"Georgia Institute of Technology","ror":"https://ror.org/01zkghx44","country_code":"US","type":"education","lineage":["https://openalex.org/I130701444"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Jie Ma","raw_affiliation_strings":["School of Mathematics, Georgia Institute of Technology, Atlanta, GA, 30332, USA","School of Mathematics, Georgia Institute of Technology, Atlanta, USA 30332"],"affiliations":[{"raw_affiliation_string":"School of Mathematics, Georgia Institute of Technology, Atlanta, GA, 30332, USA","institution_ids":["https://openalex.org/I130701444"]},{"raw_affiliation_string":"School of Mathematics, Georgia Institute of Technology, Atlanta, USA 30332","institution_ids":["https://openalex.org/I130701444"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5070536551","display_name":"Xingxing Yu","orcid":"https://orcid.org/0000-0002-6370-3163"},"institutions":[{"id":"https://openalex.org/I130701444","display_name":"Georgia Institute of Technology","ror":"https://ror.org/01zkghx44","country_code":"US","type":"education","lineage":["https://openalex.org/I130701444"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Xingxing Yu","raw_affiliation_strings":["School of Mathematics, Georgia Institute of Technology, Atlanta, GA, 30332, USA","School of Mathematics, Georgia Institute of Technology, Atlanta, USA 30332"],"affiliations":[{"raw_affiliation_string":"School of Mathematics, Georgia Institute of Technology, Atlanta, GA, 30332, USA","institution_ids":["https://openalex.org/I130701444"]},{"raw_affiliation_string":"School of Mathematics, Georgia Institute of Technology, Atlanta, USA 30332","institution_ids":["https://openalex.org/I130701444"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5065410958","display_name":"Wenan Zang","orcid":"https://orcid.org/0000-0001-6729-1760"},"institutions":[{"id":"https://openalex.org/I889458895","display_name":"University of Hong Kong","ror":"https://ror.org/02zhqgq86","country_code":"HK","type":"education","lineage":["https://openalex.org/I889458895"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"Wenan Zang","raw_affiliation_strings":["Department of Mathematics, The University of Hong Kong, Hong Kong, China"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, The University of Hong Kong, Hong Kong, China","institution_ids":["https://openalex.org/I889458895"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5007960147"],"corresponding_institution_ids":["https://openalex.org/I130701444"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":{"value":2390,"currency":"EUR","value_usd":2990},"fwci":0.6511,"has_fulltext":true,"cited_by_count":9,"citation_normalized_percentile":{"value":0.6983127,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"26","issue":"1","first_page":"127","last_page":"134"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9998999834060669,"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":0.9998999834060669,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9995999932289124,"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/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9993000030517578,"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/combinatorics","display_name":"Combinatorics","score":0.8371248841285706},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.745119571685791},{"id":"https://openalex.org/keywords/disjoint-sets","display_name":"Disjoint sets","score":0.6833099126815796},{"id":"https://openalex.org/keywords/constructive","display_name":"Constructive","score":0.6120619773864746},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.5154574513435364},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.5137506723403931},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.46152442693710327},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4536920189857483},{"id":"https://openalex.org/keywords/plane","display_name":"Plane (geometry)","score":0.44271132349967957},{"id":"https://openalex.org/keywords/theory-of-computation","display_name":"Theory of computation","score":0.4104200303554535},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.11909955739974976},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.11301776766777039},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.08187854290008545}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8371248841285706},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.745119571685791},{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.6833099126815796},{"id":"https://openalex.org/C2778701210","wikidata":"https://www.wikidata.org/wiki/Q28130034","display_name":"Constructive","level":3,"score":0.6120619773864746},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.5154574513435364},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.5137506723403931},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.46152442693710327},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4536920189857483},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.44271132349967957},{"id":"https://openalex.org/C24858836","wikidata":"https://www.wikidata.org/wiki/Q844718","display_name":"Theory of computation","level":2,"score":0.4104200303554535},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.11909955739974976},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.11301776766777039},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.08187854290008545},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/s10878-011-9440-0","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10878-011-9440-0","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10878-011-9440-0.pdf","source":{"id":"https://openalex.org/S107925523","display_name":"Journal of Combinatorial Optimization","issn_l":"1382-6905","issn":["1382-6905","1573-2886"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by-nc","license_id":"https://openalex.org/licenses/cc-by-nc","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Combinatorial Optimization","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:spr:jcomop:v:26:y:2013:i:1:d:10.1007_s10878-011-9440-0","is_oa":false,"landing_page_url":"http://link.springer.com/10.1007/s10878-011-9440-0","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},{"id":"pmh:oai:hub.hku.hk:10722/147122","is_oa":true,"landing_page_url":"http://hdl.handle.net/10722/147122","pdf_url":null,"source":{"id":"https://openalex.org/S4377196271","display_name":"The HKU Scholars Hub (University of Hong Kong)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I889458895","host_organization_name":"University of Hong Kong","host_organization_lineage":["https://openalex.org/I889458895"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"}],"best_oa_location":{"id":"doi:10.1007/s10878-011-9440-0","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10878-011-9440-0","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10878-011-9440-0.pdf","source":{"id":"https://openalex.org/S107925523","display_name":"Journal of Combinatorial Optimization","issn_l":"1382-6905","issn":["1382-6905","1573-2886"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by-nc","license_id":"https://openalex.org/licenses/cc-by-nc","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Combinatorial Optimization","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320311089","display_name":"National Security Agency","ror":"https://ror.org/0047bvr32"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2038607360.pdf","grobid_xml":"https://content.openalex.org/works/W2038607360.grobid-xml"},"referenced_works_count":11,"referenced_works":["https://openalex.org/W1491529421","https://openalex.org/W1975433230","https://openalex.org/W1980526181","https://openalex.org/W2013332890","https://openalex.org/W2032222063","https://openalex.org/W2079566953","https://openalex.org/W2332112754","https://openalex.org/W2611093227","https://openalex.org/W3084987570","https://openalex.org/W4232896595","https://openalex.org/W4313198092"],"related_works":["https://openalex.org/W2808944898","https://openalex.org/W3196207352","https://openalex.org/W2951724202","https://openalex.org/W3084261076","https://openalex.org/W1996614773","https://openalex.org/W4387820098","https://openalex.org/W2959217929","https://openalex.org/W4242866892","https://openalex.org/W84644661","https://openalex.org/W42551271"],"abstract_inverted_index":{"Let":[0],"G":[1],"be":[2,10,29],"a":[3],"plane":[4],"graph,":[5],"let":[6,25],"\u03c4(G)":[7],"(resp.":[8,16,27,35],"\u03c4\u2032(G))":[9],"the":[11,30,62],"minimum":[12],"number":[13,32],"of":[14,22,33],"vertices":[15],"edges)":[17],"that":[18,45],"meet":[19],"all":[20],"cycles":[21,37],"G,":[23],"and":[24,47],"\u03bd(G)":[26],"\u03bd\u2032(G))":[28],"maximum":[31],"vertex-disjoint":[34],"edge-disjoint)":[36],"in":[38],"G.":[39],"In":[40],"this":[41],"note":[42],"we":[43],"show":[44],"\u03c4(G)\u22643\u03bd(G)":[46],"\u03c4\u2032(G)\u22644\u03bd\u2032(G)\u22121;":[48],"our":[49],"proofs":[50],"are":[51],"constructive,":[52],"which":[53],"yield":[54],"polynomial-time":[55],"algorithms":[56],"for":[57],"finding":[58],"corresponding":[59],"objects":[60],"with":[61],"desired":[63],"properties.":[64]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2017,"cited_by_count":3},{"year":2012,"cited_by_count":1}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}