{"id":"https://openalex.org/W2132933762","doi":"https://doi.org/10.1142/s1793830912500346","title":"INJECTIVE COLORING OF PLANAR GRAPHS WITH GIRTH 7","display_name":"INJECTIVE COLORING OF PLANAR GRAPHS WITH GIRTH 7","publication_year":2012,"publication_date":"2012-06-01","ids":{"openalex":"https://openalex.org/W2132933762","doi":"https://doi.org/10.1142/s1793830912500346","mag":"2132933762"},"language":"en","primary_location":{"id":"doi:10.1142/s1793830912500346","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s1793830912500346","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/A5013840932","display_name":"Yuehua Bu","orcid":"https://orcid.org/0000-0001-9618-2248"},"institutions":[{"id":"https://openalex.org/I135237710","display_name":"Zhejiang Normal University","ror":"https://ror.org/01vevwk45","country_code":"CN","type":"education","lineage":["https://openalex.org/I135237710"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"YUEHUA BU","raw_affiliation_strings":["Department of Mathematics, Zhejiang Normal University, Zhejiang, Jinhua 321004, China","Department of Mathematics, Zhejiang Normal University, Zhejiang Jinhua 321004, China#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Zhejiang Normal University, Zhejiang, Jinhua 321004, China","institution_ids":["https://openalex.org/I135237710"]},{"raw_affiliation_string":"Department of Mathematics, Zhejiang Normal University, Zhejiang Jinhua 321004, China#TAB#","institution_ids":["https://openalex.org/I135237710"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5035924944","display_name":"Kai L\u00fc","orcid":"https://orcid.org/0000-0002-7757-4083"},"institutions":[{"id":"https://openalex.org/I135237710","display_name":"Zhejiang Normal University","ror":"https://ror.org/01vevwk45","country_code":"CN","type":"education","lineage":["https://openalex.org/I135237710"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"KAI LU","raw_affiliation_strings":["Department of Mathematics, Zhejiang Normal University, Zhejiang, Jinhua 321004, China","Department of Mathematics, Zhejiang Normal University, Zhejiang Jinhua 321004, China#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Zhejiang Normal University, Zhejiang, Jinhua 321004, China","institution_ids":["https://openalex.org/I135237710"]},{"raw_affiliation_string":"Department of Mathematics, Zhejiang Normal University, Zhejiang Jinhua 321004, China#TAB#","institution_ids":["https://openalex.org/I135237710"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5013840932"],"corresponding_institution_ids":["https://openalex.org/I135237710"],"apc_list":null,"apc_paid":null,"fwci":1.6848,"has_fulltext":false,"cited_by_count":12,"citation_normalized_percentile":{"value":0.84978866,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"04","issue":"02","first_page":"1250034","last_page":"1250034"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9983999729156494,"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":0.9983999729156494,"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":0.9939000010490417,"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":0.9663000106811523,"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":0.8282731175422668},{"id":"https://openalex.org/keywords/injective-function","display_name":"Injective function","score":0.7278937101364136},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6131377220153809},{"id":"https://openalex.org/keywords/planar-graph","display_name":"Planar graph","score":0.5240316987037659},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5023453235626221},{"id":"https://openalex.org/keywords/edge-coloring","display_name":"Edge coloring","score":0.44925791025161743},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3956993520259857},{"id":"https://openalex.org/keywords/graph-power","display_name":"Graph power","score":0.35939866304397583},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.09447532892227173}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8282731175422668},{"id":"https://openalex.org/C128107574","wikidata":"https://www.wikidata.org/wiki/Q182003","display_name":"Injective function","level":2,"score":0.7278937101364136},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6131377220153809},{"id":"https://openalex.org/C101837359","wikidata":"https://www.wikidata.org/wiki/Q547823","display_name":"Planar graph","level":3,"score":0.5240316987037659},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5023453235626221},{"id":"https://openalex.org/C123809776","wikidata":"https://www.wikidata.org/wiki/Q1050972","display_name":"Edge coloring","level":5,"score":0.44925791025161743},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3956993520259857},{"id":"https://openalex.org/C149530733","wikidata":"https://www.wikidata.org/wiki/Q5597091","display_name":"Graph power","level":4,"score":0.35939866304397583},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.09447532892227173}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s1793830912500346","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s1793830912500346","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":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":8,"referenced_works":["https://openalex.org/W1988435782","https://openalex.org/W2024469085","https://openalex.org/W2032395556","https://openalex.org/W2057330543","https://openalex.org/W2064107568","https://openalex.org/W2068103858","https://openalex.org/W2083783761","https://openalex.org/W2125862453"],"related_works":["https://openalex.org/W1492157759","https://openalex.org/W2655188380","https://openalex.org/W3089939915","https://openalex.org/W4388889440","https://openalex.org/W2963000151","https://openalex.org/W2066767025","https://openalex.org/W2742781961","https://openalex.org/W2287845327","https://openalex.org/W3184578513","https://openalex.org/W3162029291"],"abstract_inverted_index":{"An":[0],"injective":[1,36],"k-coloring":[2],"of":[3,10,16,39],"a":[4,24,53,70],"graph":[5,55,72],"G":[6,17,56,68],"is":[7,34,69],"an":[8],"assignment":[9],"k":[11],"colors":[12],"to":[13],"the":[14,35],"vertices":[15,22],"so":[18],"that":[19,66],"any":[20],"two":[21],"with":[23,57,73],"common":[25],"neighbor":[26],"receive":[27],"distinct":[28],"colors,":[29],"and":[30,77],"\u03c7":[31,45,82],"i":[32,46,83],"(G)":[33,47,84],"chromatic":[37],"number":[38],"G.":[40],"Dimitrov":[41],"et":[42],"al.":[43],"proved":[44],"\u2264":[48,85],"\u0394(G)":[49,78,86],"+":[50,87],"2":[51],"for":[52],"planar":[54,71],"g(G)":[58,74],"\u2265":[59,75,79],"7.":[60],"In":[61],"this":[62],"paper,":[63],"we":[64],"show":[65],"if":[67],"7":[76],"7,":[80],"then":[81],"1.":[88]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":3},{"year":2013,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
