{"id":"https://openalex.org/W4394619732","doi":"https://doi.org/10.1142/s1793830924300029","title":"2-Distance coloring of planar graphs with maximum degree 5","display_name":"2-Distance coloring of planar graphs with maximum degree 5","publication_year":2024,"publication_date":"2024-04-09","ids":{"openalex":"https://openalex.org/W4394619732","doi":"https://doi.org/10.1142/s1793830924300029"},"language":"en","primary_location":{"id":"doi:10.1142/s1793830924300029","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s1793830924300029","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/A5100423237","display_name":"Ming Chen","orcid":null},"institutions":[{"id":"https://openalex.org/I118574674","display_name":"Jiangsu Normal University","ror":"https://ror.org/051hvcm98","country_code":"CN","type":"education","lineage":["https://openalex.org/I118574674"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Ming Chen","raw_affiliation_strings":["School of Mathematics and Statistics, Jiangsu Normal University, Xuzhou, P. R. China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Jiangsu Normal University, Xuzhou, P. R. China","institution_ids":["https://openalex.org/I118574674"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5102020236","display_name":"Lu Jiang","orcid":"https://orcid.org/0009-0005-0370-119X"},"institutions":[{"id":"https://openalex.org/I118574674","display_name":"Jiangsu Normal University","ror":"https://ror.org/051hvcm98","country_code":"CN","type":"education","lineage":["https://openalex.org/I118574674"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Lu Jiang","raw_affiliation_strings":["School of Mathematics and Statistics, Jiangsu Normal University, Xuzhou, P. R. China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Jiangsu Normal University, Xuzhou, P. R. China","institution_ids":["https://openalex.org/I118574674"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5111174863","display_name":"Min Wang","orcid":"https://orcid.org/0009-0003-7063-1553"},"institutions":[{"id":"https://openalex.org/I118574674","display_name":"Jiangsu Normal University","ror":"https://ror.org/051hvcm98","country_code":"CN","type":"education","lineage":["https://openalex.org/I118574674"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Min Wang","raw_affiliation_strings":["Kewen College, Jiangsu Normal University, Xuzhou, P. R. China"],"affiliations":[{"raw_affiliation_string":"Kewen College, Jiangsu Normal University, Xuzhou, P. R. China","institution_ids":["https://openalex.org/I118574674"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101729105","display_name":"Shan Zhou","orcid":"https://orcid.org/0000-0002-3297-4315"},"institutions":[{"id":"https://openalex.org/I118574674","display_name":"Jiangsu Normal University","ror":"https://ror.org/051hvcm98","country_code":"CN","type":"education","lineage":["https://openalex.org/I118574674"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Shan Zhou","raw_affiliation_strings":["School of Mathematics and Statistics, Jiangsu Normal University, Xuzhou, P. R. China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Jiangsu Normal University, Xuzhou, P. R. China","institution_ids":["https://openalex.org/I118574674"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5100423237"],"corresponding_institution_ids":["https://openalex.org/I118574674"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.06030072,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"17","issue":"01","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":0.9690999984741211,"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":0.9690999984741211,"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":0.9437000155448914,"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/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9334999918937683,"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/degree","display_name":"Degree (music)","score":0.6689349412918091},{"id":"https://openalex.org/keywords/planar-graph","display_name":"Planar graph","score":0.5307443141937256},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.523457944393158},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.498044490814209},{"id":"https://openalex.org/keywords/planar","display_name":"Planar","score":0.46845507621765137},{"id":"https://openalex.org/keywords/edge-coloring","display_name":"Edge coloring","score":0.46335744857788086},{"id":"https://openalex.org/keywords/complete-coloring","display_name":"Complete coloring","score":0.43351346254348755},{"id":"https://openalex.org/keywords/brooks-theorem","display_name":"Brooks' theorem","score":0.4219141900539398},{"id":"https://openalex.org/keywords/1-planar-graph","display_name":"1-planar graph","score":0.3146429657936096},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.30357271432876587},{"id":"https://openalex.org/keywords/chordal-graph","display_name":"Chordal graph","score":0.2832060754299164},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.22262123227119446},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.13809382915496826},{"id":"https://openalex.org/keywords/computer-graphics","display_name":"Computer graphics (images)","score":0.05683279037475586},{"id":"https://openalex.org/keywords/graph-power","display_name":"Graph power","score":0.053156137466430664},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.04304736852645874}],"concepts":[{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.6689349412918091},{"id":"https://openalex.org/C101837359","wikidata":"https://www.wikidata.org/wiki/Q547823","display_name":"Planar graph","level":3,"score":0.5307443141937256},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.523457944393158},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.498044490814209},{"id":"https://openalex.org/C134786449","wikidata":"https://www.wikidata.org/wiki/Q3391255","display_name":"Planar","level":2,"score":0.46845507621765137},{"id":"https://openalex.org/C123809776","wikidata":"https://www.wikidata.org/wiki/Q1050972","display_name":"Edge coloring","level":5,"score":0.46335744857788086},{"id":"https://openalex.org/C21642379","wikidata":"https://www.wikidata.org/wiki/Q3342988","display_name":"Complete coloring","level":5,"score":0.43351346254348755},{"id":"https://openalex.org/C51658606","wikidata":"https://www.wikidata.org/wiki/Q512897","display_name":"Brooks' theorem","level":5,"score":0.4219141900539398},{"id":"https://openalex.org/C102192266","wikidata":"https://www.wikidata.org/wiki/Q4545823","display_name":"1-planar graph","level":4,"score":0.3146429657936096},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.30357271432876587},{"id":"https://openalex.org/C160446614","wikidata":"https://www.wikidata.org/wiki/Q1322892","display_name":"Chordal graph","level":3,"score":0.2832060754299164},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.22262123227119446},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.13809382915496826},{"id":"https://openalex.org/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"score":0.05683279037475586},{"id":"https://openalex.org/C149530733","wikidata":"https://www.wikidata.org/wiki/Q5597091","display_name":"Graph power","level":4,"score":0.053156137466430664},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.04304736852645874},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s1793830924300029","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s1793830924300029","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/W2035278325","https://openalex.org/W2148410650","https://openalex.org/W2795359627","https://openalex.org/W2963408654","https://openalex.org/W4205307969","https://openalex.org/W4232151508","https://openalex.org/W4311254117","https://openalex.org/W4320039150"],"related_works":["https://openalex.org/W4311345810","https://openalex.org/W2185327546","https://openalex.org/W398688634","https://openalex.org/W2352363476","https://openalex.org/W4361186694","https://openalex.org/W4320918672","https://openalex.org/W2042876012","https://openalex.org/W4229747356","https://openalex.org/W2527418013","https://openalex.org/W1993627687"],"abstract_inverted_index":{"A":[0],"2-distance":[1,26,42],"coloring":[2],"of":[3],"a":[4,7,41],"graph":[5,59],"is":[6,28,106],"proper":[8],"[Formula:":[9,32,37,43,48,60,66,69,73,76,80,84,88,101,111,120,126],"see":[10,33,38,44,49,61,67,70,74,77,81,85,89,102,112,121,127],"text]-coloring":[11],"in":[12],"which":[13,129],"any":[14],"two":[15,21],"vertices":[16],"with":[17,63],"distance":[18],"at":[19],"most":[20],"get":[22],"different":[23],"colors.":[24],"The":[25,104],"number":[27,31],"the":[29,95,99,124,131],"smallest":[30],"text]":[34,39,62,71,78,86,122,128],"such":[35],"that":[36,55,119],"has":[40],"text]-coloring,":[45],"denoted":[46],"as":[47],"text].":[50,90,103,113],"In":[51,91,114],"1977,":[52],"Wegner":[53],"conjectured":[54],"for":[56,110,123],"each":[57],"planar":[58],"maximum":[64],"degree":[65],"text],":[68,75,82],"if":[72,79,87],"and":[83],"2001,":[92],"Thomassen":[93],"supported":[94],"conjecture":[96,105],"by":[97,137],"proving":[98],"case":[100,125],"still":[107],"open":[108],"even":[109],"this":[115],"paper,":[116],"we":[117],"show":[118],"improves":[130],"upper":[132],"bound":[133],"18":[134],"recently":[135],"obtained":[136],"Hou":[138],"et":[139],"al.":[140]},"counts_by_year":[],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2025-10-10T00:00:00"}
