{"id":"https://openalex.org/W3173806834","doi":"https://doi.org/10.37236/9938","title":"Circular Chromatic Number of Signed Graphs","display_name":"Circular Chromatic Number of Signed Graphs","publication_year":2021,"publication_date":"2021-06-18","ids":{"openalex":"https://openalex.org/W3173806834","doi":"https://doi.org/10.37236/9938","mag":"3173806834"},"language":"en","primary_location":{"id":"doi:10.37236/9938","is_oa":true,"landing_page_url":"https://doi.org/10.37236/9938","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v28i2p44/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/v28i2p44/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5050560944","display_name":"Reza Naserasr","orcid":"https://orcid.org/0000-0001-6882-6034"},"institutions":[{"id":"https://openalex.org/I169173203","display_name":"D\u00e9l\u00e9gation Paris 7","ror":"https://ror.org/00bw5n526","country_code":"FR","type":"government","lineage":["https://openalex.org/I154526488","https://openalex.org/I169173203"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Reza Naserasr","raw_affiliation_strings":["universit\u00e9 PARIS DIDEROT"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"universit\u00e9 PARIS DIDEROT","institution_ids":["https://openalex.org/I169173203"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5001238118","display_name":"Zhouningxin Wang","orcid":"https://orcid.org/0000-0003-4722-4880"},"institutions":[{"id":"https://openalex.org/I204730241","display_name":"Universit\u00e9 Paris Cit\u00e9","ror":"https://ror.org/05f82e368","country_code":"FR","type":"education","lineage":["https://openalex.org/I204730241"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Zhouningxin Wang","raw_affiliation_strings":["Universit\u00e9 de Paris"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universit\u00e9 de Paris","institution_ids":["https://openalex.org/I204730241"]}]},{"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, Jinhua"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Zhejiang Normal University, Jinhua","institution_ids":["https://openalex.org/I135237710"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.9807,"has_fulltext":true,"cited_by_count":16,"citation_normalized_percentile":{"value":0.87899543,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":98},"biblio":{"volume":"28","issue":"2","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":0.9672999978065491,"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":0.9672999978065491,"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":0.9653000235557556,"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/signed-graph","display_name":"Signed graph","score":0.8748940229415894},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8687925338745117},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8067424893379211},{"id":"https://openalex.org/keywords/infimum-and-supremum","display_name":"Infimum and supremum","score":0.698116660118103},{"id":"https://openalex.org/keywords/chromatic-scale","display_name":"Chromatic scale","score":0.5861039161682129},{"id":"https://openalex.org/keywords/sigma","display_name":"Sigma","score":0.5842308402061462},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4713957607746124},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4568094313144684},{"id":"https://openalex.org/keywords/antipodal-point","display_name":"Antipodal point","score":0.4148423671722412},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1222558319568634},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.10821777582168579}],"concepts":[{"id":"https://openalex.org/C2779773260","wikidata":"https://www.wikidata.org/wiki/Q11246292","display_name":"Signed graph","level":3,"score":0.8748940229415894},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8687925338745117},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8067424893379211},{"id":"https://openalex.org/C95611797","wikidata":"https://www.wikidata.org/wiki/Q17502105","display_name":"Infimum and supremum","level":2,"score":0.698116660118103},{"id":"https://openalex.org/C196956537","wikidata":"https://www.wikidata.org/wiki/Q202021","display_name":"Chromatic scale","level":2,"score":0.5861039161682129},{"id":"https://openalex.org/C2778049214","wikidata":"https://www.wikidata.org/wiki/Q7512234","display_name":"Sigma","level":2,"score":0.5842308402061462},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4713957607746124},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4568094313144684},{"id":"https://openalex.org/C70943382","wikidata":"https://www.wikidata.org/wiki/Q505356","display_name":"Antipodal point","level":2,"score":0.4148423671722412},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1222558319568634},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.10821777582168579},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.37236/9938","is_oa":true,"landing_page_url":"https://doi.org/10.37236/9938","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v28i2p44/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:10.37236/9938","is_oa":true,"landing_page_url":"https://doi.org/10.37236/9938","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v28i2p44/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":[{"id":"https://openalex.org/G1856762535","display_name":null,"funder_award_id":"11971438","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2557521919","display_name":"International Doctoral Training in Mathematical Sciences in Paris","funder_award_id":"754362","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G434337789","display_name":null,"funder_award_id":"HORIZON2020","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G4434883565","display_name":null,"funder_award_id":"12026248","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5490956810","display_name":null,"funder_award_id":"U20A2068","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6803667113","display_name":null,"funder_award_id":"ANR-17","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G709147851","display_name":null,"funder_award_id":"NSFC 11971438","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320320883","display_name":"Agence Nationale de la Recherche","ror":"https://ror.org/00rbzpz17"},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3173806834.pdf","grobid_xml":"https://content.openalex.org/works/W3173806834.grobid-xml"},"referenced_works_count":32,"referenced_works":["https://openalex.org/W136992432","https://openalex.org/W1508755082","https://openalex.org/W1609788678","https://openalex.org/W1679590246","https://openalex.org/W1855957319","https://openalex.org/W1976047413","https://openalex.org/W1982514465","https://openalex.org/W1995168815","https://openalex.org/W1998195498","https://openalex.org/W2039256426","https://openalex.org/W2060050269","https://openalex.org/W2108916804","https://openalex.org/W2132677029","https://openalex.org/W2161214751","https://openalex.org/W2200162493","https://openalex.org/W2953618197","https://openalex.org/W2963764468","https://openalex.org/W2964254008","https://openalex.org/W2964620984","https://openalex.org/W3041680544","https://openalex.org/W3082346901","https://openalex.org/W3082456181","https://openalex.org/W3122614101","https://openalex.org/W4230039044","https://openalex.org/W4234352366","https://openalex.org/W4240418723","https://openalex.org/W4248657228","https://openalex.org/W4249144802","https://openalex.org/W4287599839","https://openalex.org/W6637239020","https://openalex.org/W6639272271","https://openalex.org/W6767505063"],"related_works":["https://openalex.org/W4390723618","https://openalex.org/W257437400","https://openalex.org/W4378170351","https://openalex.org/W2057367302","https://openalex.org/W4287811145","https://openalex.org/W1980444514","https://openalex.org/W4383295048","https://openalex.org/W4220685885","https://openalex.org/W2951225080","https://openalex.org/W2077368329"],"abstract_inverted_index":{"A":[0],"signed":[1,41,56,60,133,158,183,203,214,231,257,274],"graph":[2,12,61,134,153,260,275],"is":[3,10,24,74,137,170,265,268],"a":[4,11,25,34,59,68,81,132,148,152,171,256,273,282,285],"pair":[5],"$(G,":[6,62,72,135,145],"\\sigma)$,":[7],"where":[8],"$G$":[9,33,90,163],"(loops":[13],"and":[14,18,103,110,115,185,201,209,251,270,279,290],"multi":[15],"edges":[16],"allowed)":[17],"$\\sigma:":[19],"E(G)":[20],"\\to":[21],"\\{+,":[22],"-\\}$":[23],"signature":[26,172],"which":[27,144],"assigns":[28],"to":[29,55,86,164,284],"each":[30],"edge":[31,95],"of":[32,38,40,53,71,78,80,83,89,97,118,131,140,162,173,179,182,207,218,221,229,235,238,241,287],"sign.":[35],"Various":[36],"notions":[37],"coloring":[39,52,181],"graphs":[42,54,184,237,250],"have":[43,105,120],"been":[44],"studied.":[45],"In":[46,223],"this":[47],"paper,":[48],"we":[49,155,225],"extend":[50],"circular":[51,69,126,149,159,180,198,204,215,232,262],"graphs.":[57,222,253],"Given":[58],"\\sigma)$":[63,73,130,136,146],"with":[64],"no":[65],"positive":[66],"loop,":[67],"$r$-coloring":[70],"an":[75],"assignment":[76],"$\\psi$":[77],"points":[79],"circle":[82],"circumference":[84],"$r$":[85,142],"the":[87,116,138,157,194,197,202,213,227,230],"vertices":[88],"such":[91],"that":[92],"for":[93,143,188,212],"every":[94],"$e=uv$":[96],"$G$,":[98,154],"if":[99,111],"$\\sigma(e)=+$,":[100],"then":[101,113],"$\\psi(u)$":[102,119],"$\\psi(v)$":[104,114],"distance":[106,121],"at":[107,122],"least":[108,123],"$1$,":[109],"$\\sigma(e)=-$,":[112],"antipodal":[117],"$1$.":[124],"The":[125],"chromatic":[127,160,199,205,216,233,263],"number":[128,161,200,206,217,234,264],"$\\chi_c(G,":[129,190],"infimum":[139],"those":[141],"admits":[147],"$r$-coloring.":[150],"For":[151],"define":[156],"be":[165],"$\\max\\{\\chi_c(G,":[166],"\\sigma):":[167],"\\sigma":[168],"\\text{":[169],"$G$}\\}$.":[174],"We":[175,192,254],"study":[176],"basic":[177],"properties":[178],"develop":[186],"tools":[187],"calculating":[189],"\\sigma)$.":[191],"explore":[193],"relation":[195],"between":[196],"graphs,":[208,245,247],"present":[210],"bounds":[211],"some":[219],"families":[220],"particular,":[224],"determine":[226],"supremum":[228],"$k$-chromatic":[236],"large":[239],"girth,":[240],"simple":[242,248,259],"bipartite":[243],"planar":[244,258],"$d$-degenerate":[246],"outerplanar":[249],"series-parallel":[252],"construct":[255],"whose":[261],"$4+\\frac{2}{3}$.":[266],"This":[267],"based":[269],"improves":[271],"on":[272],"built":[276],"by":[277],"Kardos":[278],"Narboni":[280],"as":[281],"counterexample":[283],"conjecture":[286],"M\u00e1\u010dajov\u00e1,":[288],"Raspaud,":[289],"\u0160koviera.":[291]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":4}],"updated_date":"2026-08-04T08:18:43.703281","created_date":"2025-10-10T00:00:00"}