{"id":"https://openalex.org/W1633245187","doi":"https://doi.org/10.46298/dmtcs.1268","title":"Strong parity vertex coloring of plane graphs","display_name":"Strong parity vertex coloring of plane graphs","publication_year":2014,"publication_date":"2014-03-20","ids":{"openalex":"https://openalex.org/W1633245187","doi":"https://doi.org/10.46298/dmtcs.1268","mag":"1633245187"},"language":"en","primary_location":{"id":"doi:10.46298/dmtcs.1268","is_oa":true,"landing_page_url":"https://doi.org/10.46298/dmtcs.1268","pdf_url":"https://dmtcs.episciences.org/1268/pdf","source":{"id":"https://openalex.org/S200334879","display_name":"Discrete Mathematics & Theoretical Computer Science","issn_l":"1365-8050","issn":["1365-8050","1462-7264"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4328141799","host_organization_name":"French association","host_organization_lineage":["https://openalex.org/P4328141799"],"host_organization_lineage_names":["French association"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete Mathematics & Theoretical Computer Science","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://dmtcs.episciences.org/1268/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5000051529","display_name":"Tom\u00e1\u0161 Kaiser","orcid":"https://orcid.org/0000-0003-0448-0171"},"institutions":[{"id":"https://openalex.org/I4210155092","display_name":"Czech Academy of Sciences, Institute of Computer Science","ror":"https://ror.org/0496n6574","country_code":"CZ","type":"facility","lineage":["https://openalex.org/I202391551","https://openalex.org/I4210155092"]}],"countries":["CZ"],"is_corresponding":false,"raw_author_name":"Tomas Kaiser","raw_affiliation_strings":["department of mathematics and institute of computer science","department of mathematics and institute of computer science (Czech Republic)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"department of mathematics and institute of computer science","institution_ids":[]},{"raw_affiliation_string":"department of mathematics and institute of computer science (Czech Republic)","institution_ids":["https://openalex.org/I4210155092"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5037574166","display_name":"Ond\u0159ej Ruck\u00fd","orcid":null},"institutions":[{"id":"https://openalex.org/I4210155092","display_name":"Czech Academy of Sciences, Institute of Computer Science","ror":"https://ror.org/0496n6574","country_code":"CZ","type":"facility","lineage":["https://openalex.org/I202391551","https://openalex.org/I4210155092"]}],"countries":["CZ"],"is_corresponding":false,"raw_author_name":"Ondrej Rucky","raw_affiliation_strings":["department of mathematics and institute of computer science","department of mathematics and institute of computer science (Czech Republic)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"department of mathematics and institute of computer science","institution_ids":[]},{"raw_affiliation_string":"department of mathematics and institute of computer science (Czech Republic)","institution_ids":["https://openalex.org/I4210155092"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5104102374","display_name":"Mat\u011bj Stehl\u0131\u0301k","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Matej Stehlik","raw_affiliation_strings":["Optimisation Combinatoire"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Optimisation Combinatoire","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5083674096","display_name":"Riste \u0160krekovski","orcid":"https://orcid.org/0000-0001-6851-3214"},"institutions":[{"id":"https://openalex.org/I153976015","display_name":"University of Ljubljana","ror":"https://ror.org/05njb9z20","country_code":"SI","type":"education","lineage":["https://openalex.org/I153976015"]},{"id":"https://openalex.org/I4210106342","display_name":"Institute of Mathematics, Physics, and Mechanics","ror":"https://ror.org/01eb3qa50","country_code":"SI","type":"facility","lineage":["https://openalex.org/I4210106342"]}],"countries":["SI"],"is_corresponding":false,"raw_author_name":"Riste \u0160krekovski","raw_affiliation_strings":["Faculty of Mathematics and Physics [Ljubljana]","FMF - Faculty of Mathematics and Physics [Ljubljana] (Jadranska ulica 19, SI-1000 Ljubljana, Slovenia - Slovenia)"],"raw_orcid":"https://orcid.org/0000-0001-6851-3214","affiliations":[{"raw_affiliation_string":"Faculty of Mathematics and Physics [Ljubljana]","institution_ids":["https://openalex.org/I4210106342"]},{"raw_affiliation_string":"FMF - Faculty of Mathematics and Physics [Ljubljana] (Jadranska ulica 19, SI-1000 Ljubljana, Slovenia - Slovenia)","institution_ids":["https://openalex.org/I153976015"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.7147,"has_fulltext":true,"cited_by_count":7,"citation_normalized_percentile":{"value":0.69662844,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"Vol. 16 no. 1","issue":"Graph Theory","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12541","display_name":"Graph Labeling and Dimension Problems","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/T12541","display_name":"Graph Labeling and Dimension Problems","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/T10374","display_name":"Advanced Graph Theory Research","score":0.9926999807357788,"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/T11797","display_name":"graph theory and CDMA systems","score":0.9876000285148621,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7884221076965332},{"id":"https://openalex.org/keywords/fractional-coloring","display_name":"Fractional coloring","score":0.7570945620536804},{"id":"https://openalex.org/keywords/graph-coloring","display_name":"Graph coloring","score":0.7163281440734863},{"id":"https://openalex.org/keywords/complete-coloring","display_name":"Complete coloring","score":0.7023115754127502},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6428520679473877},{"id":"https://openalex.org/keywords/list-coloring","display_name":"List coloring","score":0.5845516920089722},{"id":"https://openalex.org/keywords/parity","display_name":"Parity (physics)","score":0.5812982320785522},{"id":"https://openalex.org/keywords/edge-coloring","display_name":"Edge coloring","score":0.5708844065666199},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.5181878209114075},{"id":"https://openalex.org/keywords/brooks-theorem","display_name":"Brooks' theorem","score":0.5016767978668213},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.46617889404296875},{"id":"https://openalex.org/keywords/greedy-coloring","display_name":"Greedy coloring","score":0.4420255720615387},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.4301200211048126},{"id":"https://openalex.org/keywords/graph-power","display_name":"Graph power","score":0.37724781036376953},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.32720690965652466},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.18586552143096924},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.14579865336418152}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7884221076965332},{"id":"https://openalex.org/C158319403","wikidata":"https://www.wikidata.org/wiki/Q5477527","display_name":"Fractional coloring","level":5,"score":0.7570945620536804},{"id":"https://openalex.org/C76946457","wikidata":"https://www.wikidata.org/wiki/Q504843","display_name":"Graph coloring","level":3,"score":0.7163281440734863},{"id":"https://openalex.org/C21642379","wikidata":"https://www.wikidata.org/wiki/Q3342988","display_name":"Complete coloring","level":5,"score":0.7023115754127502},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6428520679473877},{"id":"https://openalex.org/C199594403","wikidata":"https://www.wikidata.org/wiki/Q1130404","display_name":"List coloring","level":5,"score":0.5845516920089722},{"id":"https://openalex.org/C2777151079","wikidata":"https://www.wikidata.org/wiki/Q141160","display_name":"Parity (physics)","level":2,"score":0.5812982320785522},{"id":"https://openalex.org/C123809776","wikidata":"https://www.wikidata.org/wiki/Q1050972","display_name":"Edge coloring","level":5,"score":0.5708844065666199},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.5181878209114075},{"id":"https://openalex.org/C51658606","wikidata":"https://www.wikidata.org/wiki/Q512897","display_name":"Brooks' theorem","level":5,"score":0.5016767978668213},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.46617889404296875},{"id":"https://openalex.org/C38767284","wikidata":"https://www.wikidata.org/wiki/Q5601715","display_name":"Greedy coloring","level":5,"score":0.4420255720615387},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.4301200211048126},{"id":"https://openalex.org/C149530733","wikidata":"https://www.wikidata.org/wiki/Q5597091","display_name":"Graph power","level":4,"score":0.37724781036376953},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.32720690965652466},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.18586552143096924},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.14579865336418152},{"id":"https://openalex.org/C109214941","wikidata":"https://www.wikidata.org/wiki/Q18334","display_name":"Particle physics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.46298/dmtcs.1268","is_oa":true,"landing_page_url":"https://doi.org/10.46298/dmtcs.1268","pdf_url":"https://dmtcs.episciences.org/1268/pdf","source":{"id":"https://openalex.org/S200334879","display_name":"Discrete Mathematics & Theoretical Computer Science","issn_l":"1365-8050","issn":["1365-8050","1462-7264"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4328141799","host_organization_name":"French association","host_organization_lineage":["https://openalex.org/P4328141799"],"host_organization_lineage_names":["French association"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete Mathematics & Theoretical Computer Science","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-01063684v1","is_oa":false,"landing_page_url":"https://hal.science/hal-01063684","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Discrete Mathematics and Theoretical Computer Science, 2014, Vol. 16 no. 1 (1), pp.143-158. ⟨10.46298/dmtcs.1268⟩","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:doaj.org/article:1a6f0cefe9a8463db981f7ec347ffcf6","is_oa":false,"landing_page_url":"https://doaj.org/article/1a6f0cefe9a8463db981f7ec347ffcf6","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Discrete Mathematics & Theoretical Computer Science, Vol Vol. 16 no. 1, Iss Graph Theory (2014)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.46298/dmtcs.1268","is_oa":true,"landing_page_url":"https://doi.org/10.46298/dmtcs.1268","pdf_url":"https://dmtcs.episciences.org/1268/pdf","source":{"id":"https://openalex.org/S200334879","display_name":"Discrete Mathematics & Theoretical Computer Science","issn_l":"1365-8050","issn":["1365-8050","1462-7264"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4328141799","host_organization_name":"French association","host_organization_lineage":["https://openalex.org/P4328141799"],"host_organization_lineage_names":["French association"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete Mathematics & Theoretical Computer Science","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G5566021001","display_name":null,"funder_award_id":"P202/12/G061","funder_id":"https://openalex.org/F4320321006","funder_display_name":"Grantov\u00e1 Agentura \u010cesk\u00e9 Republiky"},{"id":"https://openalex.org/G7564109755","display_name":null,"funder_award_id":"201/09/0197","funder_id":"https://openalex.org/F4320321006","funder_display_name":"Grantov\u00e1 Agentura \u010cesk\u00e9 Republiky"},{"id":"https://openalex.org/G8266550106","display_name":null,"funder_award_id":"P1-00383","funder_id":"https://openalex.org/F4320322554","funder_display_name":"Javna Agencija za Raziskovalno Dejavnost RS"}],"funders":[{"id":"https://openalex.org/F4320321006","display_name":"Grantov\u00e1 Agentura \u010cesk\u00e9 Republiky","ror":"https://ror.org/01pv73b02"},{"id":"https://openalex.org/F4320322554","display_name":"Javna Agencija za Raziskovalno Dejavnost RS","ror":"https://ror.org/059bp8k51"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1633245187.pdf","grobid_xml":"https://content.openalex.org/works/W1633245187.grobid-xml"},"referenced_works_count":5,"referenced_works":["https://openalex.org/W1986731394","https://openalex.org/W2022762479","https://openalex.org/W2024733865","https://openalex.org/W2054460597","https://openalex.org/W2798588639"],"related_works":["https://openalex.org/W4311345810","https://openalex.org/W4297911588","https://openalex.org/W2585997002","https://openalex.org/W3169197204","https://openalex.org/W4296943582","https://openalex.org/W3157287446","https://openalex.org/W4212987857","https://openalex.org/W2175082514","https://openalex.org/W151506147","https://openalex.org/W1542397451"],"abstract_inverted_index":{"Graph":[0,69],"Theory":[1,70],"A":[2],"strong":[3,45],"parity":[4,46],"vertex":[5,47],"coloring":[6,14,48,54],"of":[7,15,30,32,63],"a":[8,13,44,61],"2-connected":[9,39],"plane":[10,41],"graph":[11,42],"is":[12,22,57],"the":[16,53],"vertices":[17,31],"such":[18],"that":[19,37,80],"every":[20,38],"face":[21],"incident":[23],"with":[24,49],"zero":[25],"or":[26],"an":[27],"odd":[28],"number":[29],"each":[33],"color.":[34],"We":[35,75],"prove":[36],"loopless":[40],"has":[43],"97":[50],"colors.":[51],"Moreover":[52],"we":[55],"construct":[56],"proper.":[58],"This":[59],"proves":[60],"conjecture":[62],"Czap":[64],"and":[65],"Jendrol'":[66],"[Discuss.":[67],"Math.":[68],"29":[71],"(2009),":[72],"pp.":[73],"521-543.].":[74],"also":[76],"provide":[77],"examples":[78],"showing":[79],"eight":[81],"colors":[82],"may":[83],"be":[84],"necessary":[85],"(ten":[86],"when":[87],"restricted":[88],"to":[89],"proper":[90],"colorings).":[91]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}