{"id":"https://openalex.org/W2766027452","doi":"https://doi.org/10.37236/5555","title":"A Note on Chromatic Number and Induced Odd Cycles","display_name":"A Note on Chromatic Number and Induced Odd Cycles","publication_year":2017,"publication_date":"2017-11-03","ids":{"openalex":"https://openalex.org/W2766027452","doi":"https://doi.org/10.37236/5555","mag":"2766027452"},"language":"en","primary_location":{"id":"doi:10.37236/5555","is_oa":true,"landing_page_url":"https://doi.org/10.37236/5555","pdf_url":null,"source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://doi.org/10.37236/5555","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5005438969","display_name":"Baogang Xu","orcid":"https://orcid.org/0000-0003-0435-6103"},"institutions":[{"id":"https://openalex.org/I152031979","display_name":"Nanjing Normal University","ror":"https://ror.org/036trcv74","country_code":"CN","type":"education","lineage":["https://openalex.org/I152031979"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Baogang Xu","raw_affiliation_strings":["School of Mathematical Sciences\r\nNanjing Normal University","School of Mathematical Sciences\nNanjing Normal University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences\r\nNanjing Normal University","institution_ids":["https://openalex.org/I152031979"]},{"raw_affiliation_string":"School of Mathematical Sciences\nNanjing Normal University","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5077977616","display_name":"Gexin Yu","orcid":"https://orcid.org/0000-0001-5898-7344"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Gexin Yu","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5109172116","display_name":"Xiaoya Zha","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Xiaoya Zha","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.1863155,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":96,"max":98},"biblio":{"volume":"24","issue":"4","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9761999845504761,"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":0.9761999845504761,"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":0.9689000248908997,"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9345999956130981,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.9137255549430847},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8217836022377014},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.6497272849082947},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5167831182479858},{"id":"https://openalex.org/keywords/bipartite-graph","display_name":"Bipartite graph","score":0.5116105675697327},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.502288818359375},{"id":"https://openalex.org/keywords/chromatic-scale","display_name":"Chromatic scale","score":0.4644230902194977}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.9137255549430847},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8217836022377014},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.6497272849082947},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5167831182479858},{"id":"https://openalex.org/C197657726","wikidata":"https://www.wikidata.org/wiki/Q174733","display_name":"Bipartite graph","level":3,"score":0.5116105675697327},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.502288818359375},{"id":"https://openalex.org/C196956537","wikidata":"https://www.wikidata.org/wiki/Q202021","display_name":"Chromatic scale","level":2,"score":0.4644230902194977}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.37236/5555","is_oa":true,"landing_page_url":"https://doi.org/10.37236/5555","pdf_url":null,"source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},{"id":"pmh:oai:scholarworks.wm.edu:aspubs-1159","is_oa":false,"landing_page_url":"https://scholarworks.wm.edu/aspubs/159","pdf_url":null,"source":{"id":"https://openalex.org/S4306401254","display_name":"W&M Publish (College of William & Mary)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I16285277","host_organization_name":"William & Mary","host_organization_lineage":["https://openalex.org/I16285277"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Arts & Sciences Articles","raw_type":"text"}],"best_oa_location":{"id":"doi:10.37236/5555","is_oa":true,"landing_page_url":"https://doi.org/10.37236/5555","pdf_url":null,"source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2371352078","https://openalex.org/W2953461625","https://openalex.org/W2077383796","https://openalex.org/W2080136900","https://openalex.org/W2372768926","https://openalex.org/W2999799752","https://openalex.org/W2567825307","https://openalex.org/W2054458431","https://openalex.org/W2950817880","https://openalex.org/W3178681420"],"abstract_inverted_index":{"An":[0],"odd":[1,6,30,48,71],"hole":[2],"is":[3],"an":[4],"induced":[5],"cycle":[7],"of":[8,19,73,96,100,102],"length":[9,74],"at":[10,75,88],"least":[11,76],"5.":[12],"Scott":[13],"and":[14,21,38,68,81,91,118],"Seymour":[15,37],"confirmed":[16],"a":[17,25,60,109],"conjecture":[18],"Gy\u00e1rf\u00e1s":[20],"proved":[22],"that":[23,41,58],"if":[24,42,59,84],"graph":[26,61],"$G$":[27,43,62,85],"has":[28,44,63,69,86],"no":[29,70],"holes":[31,49,72],"then":[32,50,78],"$\\chi(G)\\le":[33,51,79,82],"2^{2^{\\omega(G)+2}}$.":[34],"Chudnovsky,":[35],"Robertson,":[36],"Thomas":[39],"showed":[40],"neither":[45,64],"$K_4$":[46],"nor":[47,66],"4$.":[52],"In":[53],"this":[54],"note,":[55],"we":[56],"show":[57],"triangles":[65],"quadrilaterals,":[67],"7,":[77],"4$":[80],"3$":[83],"radius":[87],"most":[89],"$3$,":[90],"for":[92],"each":[93],"vertex":[94],"$u$":[95,107],"$G$,":[97],"the":[98,103],"set":[99],"vertices":[101],"same":[104],"distance":[105],"to":[106],"induces":[108],"bipartite":[110],"subgraph.":[111],"This":[112],"answers":[113],"some":[114],"questions":[115],"in":[116],"Plummer":[117],"Zha":[119],"(2014).":[120]},"counts_by_year":[{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":3}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}