{"id":"https://openalex.org/W3083096111","doi":"https://doi.org/10.37236/9338","title":"$4$-Colouring of Generalized Signed Planar Graphs","display_name":"$4$-Colouring of Generalized Signed Planar Graphs","publication_year":2020,"publication_date":"2020-08-21","ids":{"openalex":"https://openalex.org/W3083096111","doi":"https://doi.org/10.37236/9338","mag":"3083096111"},"language":"en","primary_location":{"id":"doi:10.37236/9338","is_oa":true,"landing_page_url":"https://doi.org/10.37236/9338","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v27i3p31/pdf","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://www.combinatorics.org/ojs/index.php/eljc/article/download/v27i3p31/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5077162250","display_name":"Yiting Jiang","orcid":"https://orcid.org/0000-0003-2338-4732"},"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":"Yiting Jiang","raw_affiliation_strings":["Department of Mathematics Zhejiang Normal University Jinhua, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics Zhejiang Normal University Jinhua, China","institution_ids":["https://openalex.org/I135237710"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5020969478","display_name":"Xuding Zhu","orcid":"https://orcid.org/0000-0002-5502-5390"},"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":"Xuding Zhu","raw_affiliation_strings":["Zhejiang Normal University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Zhejiang Normal University","institution_ids":["https://openalex.org/I135237710"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.3122,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.57528525,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":95},"biblio":{"volume":"27","issue":"3","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.7544999718666077,"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"}},"topics":[{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.7544999718666077,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.7287999987602234,"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":0.8776658773422241},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8118216395378113},{"id":"https://openalex.org/keywords/permutation","display_name":"Permutation (music)","score":0.6047917604446411},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5313632488250732},{"id":"https://openalex.org/keywords/sigma","display_name":"Sigma","score":0.5263558626174927},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.5045381784439087},{"id":"https://openalex.org/keywords/signature","display_name":"Signature (topology)","score":0.47034838795661926},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4566357433795929},{"id":"https://openalex.org/keywords/arc","display_name":"Arc (geometry)","score":0.4198697805404663},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.058366358280181885}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8776658773422241},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8118216395378113},{"id":"https://openalex.org/C21308566","wikidata":"https://www.wikidata.org/wiki/Q7169365","display_name":"Permutation (music)","level":2,"score":0.6047917604446411},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5313632488250732},{"id":"https://openalex.org/C2778049214","wikidata":"https://www.wikidata.org/wiki/Q7512234","display_name":"Sigma","level":2,"score":0.5263558626174927},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.5045381784439087},{"id":"https://openalex.org/C2779696439","wikidata":"https://www.wikidata.org/wiki/Q7512811","display_name":"Signature (topology)","level":2,"score":0.47034838795661926},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4566357433795929},{"id":"https://openalex.org/C83415579","wikidata":"https://www.wikidata.org/wiki/Q161973","display_name":"Arc (geometry)","level":2,"score":0.4198697805404663},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.058366358280181885},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.37236/9338","is_oa":true,"landing_page_url":"https://doi.org/10.37236/9338","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v27i3p31/pdf","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"}],"best_oa_location":{"id":"doi:10.37236/9338","is_oa":true,"landing_page_url":"https://doi.org/10.37236/9338","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v27i3p31/pdf","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":[{"id":"https://openalex.org/F4320321106","display_name":"Ministry of Education of the People's Republic of China","ror":"https://ror.org/01mv9t934"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3083096111.pdf","grobid_xml":"https://content.openalex.org/works/W3083096111.grobid-xml"},"referenced_works_count":8,"referenced_works":["https://openalex.org/W2079944966","https://openalex.org/W2196486868","https://openalex.org/W2212115383","https://openalex.org/W2901656151","https://openalex.org/W2963764468","https://openalex.org/W2964254008","https://openalex.org/W2964620984","https://openalex.org/W4286482669"],"related_works":["https://openalex.org/W3162204513","https://openalex.org/W2544839741","https://openalex.org/W2371138613","https://openalex.org/W2048963458","https://openalex.org/W43109613","https://openalex.org/W2359952343","https://openalex.org/W2080152487","https://openalex.org/W1671124163","https://openalex.org/W4287905741","https://openalex.org/W4280528977"],"abstract_inverted_index":{"Assume":[0],"$G$":[1,18,30,52],"is":[2,7,19,26,36,53,64,86,109,126,132,149,173],"a":[3,8,20,37,45,65,87,114,119,144,174],"graph":[4,108],"and":[5,31,140,152],"$S$":[6,103,116,146],"set":[9],"of":[10,12,17,29,61,77,84,90,104,117,168,176],"permutations":[11],"positive":[13],"integers.":[14],"An":[15],"$S$-signature":[16,58],"pair":[21],"$(D,":[22,59],"\\sigma)$,":[23],"where":[24],"$D$":[25],"an":[27],"orientation":[28],"$\\sigma:":[32],"E(D)":[33],"\\to":[34,69],"S$":[35],"mapping":[38,66],"which":[39,101],"assigns":[40],"to":[41,100,128,163],"each":[42,74],"arc":[43,75],"$e=(u,v)$":[44,76],"permutation":[46],"$\\sigma(e)$":[47],"in":[48],"$S$.":[49],"We":[50,111],"say":[51],"$S$-$k$-colourable":[54,85],"if":[55,151,154],"for":[56,73],"any":[57],"\\sigma)$":[60],"$G$,":[62,78],"there":[63],"$f:":[67],"V(G)":[68],"[k]$":[70],"such":[71,113],"that":[72,130,143],"$\\sigma(e)(f(u))":[79],"\\ne":[80],"f(v)$.":[81],"The":[82,122],"concept":[83],"common":[88],"generalization":[89],"many":[91],"colouring":[92],"concepts.":[93],"This":[94],"paper":[95],"studies":[96],"the":[97],"problem":[98],"as":[99],"subsets":[102],"$S_4$,":[105],"every":[106,165],"planar":[107],"$S$-$4$-colourable.":[110],"call":[112],"subset":[115,145,167,175],"$S_4$":[118,169],"good":[120,150,166],"subset.":[121],"Four":[123],"Colour":[124],"Theorem":[125],"equivalent":[127],"saying":[129],"$S=\\{id\\}$":[131],"good.":[133],"It":[134],"was":[135],"proved":[136],"by":[137],"Jin,":[138],"Wong":[139],"Zhu":[141],"(arXiv:1811.08584)":[142],"containing":[147,171],"$id$":[148,172],"only":[153],"$S=\\{id\\}$.":[155],"In":[156],"this":[157],"paper,":[158],"we":[159],"prove":[160],"that,":[161],"up":[162],"conjugation,":[164],"not":[170],"$\\{(12),(34),(12)(34)\\}$.":[177]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2019,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
