{"id":"https://openalex.org/W3197941730","doi":"https://doi.org/10.37236/10563","title":"Dense Eulerian Graphs are $(1, 3)$-Choosable","display_name":"Dense Eulerian Graphs are $(1, 3)$-Choosable","publication_year":2022,"publication_date":"2022-06-16","ids":{"openalex":"https://openalex.org/W3197941730","doi":"https://doi.org/10.37236/10563","mag":"3197941730"},"language":"en","primary_location":{"id":"doi:10.37236/10563","is_oa":true,"landing_page_url":"https://doi.org/10.37236/10563","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v29i2p54/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/v29i2p54/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5023724621","display_name":"Huajing Lu","orcid":"https://orcid.org/0000-0002-5788-8827"},"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":"Huajing Lu","raw_affiliation_strings":["Zhejiang Normal University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Zhejiang Normal University","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":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I135237710"],"apc_list":null,"apc_paid":null,"fwci":0.1437,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.43126779,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"29","issue":"2","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12541","display_name":"Graph Labeling and Dimension Problems","score":1.0,"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/T12541","display_name":"Graph Labeling and Dimension Problems","score":1.0,"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/T11476","display_name":"Graph theory and applications","score":0.986299991607666,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.982200026512146,"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":0.8282370567321777},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7856476306915283},{"id":"https://openalex.org/keywords/eulerian-path","display_name":"Eulerian path","score":0.7042244672775269},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.6956884264945984},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.6138125061988831},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.4775617718696594},{"id":"https://openalex.org/keywords/weighting","display_name":"Weighting","score":0.44141411781311035},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3692191541194916},{"id":"https://openalex.org/keywords/lagrangian","display_name":"Lagrangian","score":0.09116700291633606},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.08716312050819397}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8282370567321777},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7856476306915283},{"id":"https://openalex.org/C43058520","wikidata":"https://www.wikidata.org/wiki/Q624580","display_name":"Eulerian path","level":3,"score":0.7042244672775269},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.6956884264945984},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.6138125061988831},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.4775617718696594},{"id":"https://openalex.org/C183115368","wikidata":"https://www.wikidata.org/wiki/Q856577","display_name":"Weighting","level":2,"score":0.44141411781311035},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3692191541194916},{"id":"https://openalex.org/C53469067","wikidata":"https://www.wikidata.org/wiki/Q505735","display_name":"Lagrangian","level":2,"score":0.09116700291633606},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08716312050819397},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.37236/10563","is_oa":true,"landing_page_url":"https://doi.org/10.37236/10563","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v29i2p54/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:10.37236/10563","is_oa":true,"landing_page_url":"https://doi.org/10.37236/10563","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v29i2p54/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":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3197941730.pdf","grobid_xml":"https://content.openalex.org/works/W3197941730.grobid-xml"},"referenced_works_count":25,"referenced_works":["https://openalex.org/W1855200107","https://openalex.org/W1964459877","https://openalex.org/W1972913697","https://openalex.org/W1998456137","https://openalex.org/W2005117665","https://openalex.org/W2017934789","https://openalex.org/W2063812540","https://openalex.org/W2075047823","https://openalex.org/W2082218697","https://openalex.org/W2096599569","https://openalex.org/W2101489005","https://openalex.org/W2113432752","https://openalex.org/W2604332568","https://openalex.org/W2895265941","https://openalex.org/W2911280162","https://openalex.org/W2963062175","https://openalex.org/W3080399590","https://openalex.org/W3127740257","https://openalex.org/W4242583105","https://openalex.org/W4293999390","https://openalex.org/W6600042225","https://openalex.org/W6604381581","https://openalex.org/W6606030146","https://openalex.org/W6606719265","https://openalex.org/W6612059152"],"related_works":["https://openalex.org/W2180954594","https://openalex.org/W2052835778","https://openalex.org/W2049003611","https://openalex.org/W2127804977","https://openalex.org/W2108418243","https://openalex.org/W164103134","https://openalex.org/W2787352659","https://openalex.org/W4206560911","https://openalex.org/W1970611213","https://openalex.org/W1707372784"],"abstract_inverted_index":{"A":[0],"graph":[1,105,126],"$G$":[2,86,95,106,127],"is":[3,39,96,117,134],"total":[4,10,42,97,118,135],"weight":[5,98,119,136],"$(k,k')$-choosable":[6],"if":[7,85],"for":[8,55,66],"any":[9,125],"list":[11],"assignment":[12],"$L$":[13],"which":[14],"assigns":[15],"to":[16],"each":[17,28,56,67],"vertex":[18],"$v$":[19],"a":[20,31,40,45,101],"set":[21,32],"$L(v)$":[22],"of":[23,34,70,91,107],"$k$":[24],"real":[25,36],"numbers,":[26,37],"and":[27,65,110],"edge":[29,68],"$e$":[30],"$L(e)$":[33],"$k'$":[35],"there":[38],"proper":[41],"$L$-weighting,":[43],"i.e.,":[44],"mapping":[46],"$f:":[47],"V(G)":[48,59],"\\cup":[49,60],"E(G)":[50],"\\to":[51],"\\mathbb{R}$":[52],"such":[53],"that":[54,84,124],"$z":[57],"\\in":[58,63,73,77],"E(G)$,":[61],"$f(z)":[62],"L(z)$,":[64],"$uv$":[69],"$G$,":[71],"$\\sum_{e":[72],"E(u)}f(e)+f(u)":[74],"\\ne":[75],"\\sum_{e":[76],"E(v)}f(e)":[78],"+":[79],"f(v)$.":[80],"This":[81],"paper":[82],"proves":[83],"decomposes":[87],"into":[88],"complete":[89],"graphs":[90],"odd":[92],"order,":[93],"then":[94],"$(1,3)$-choosable.":[99,120],"As":[100],"consequence,":[102],"every":[103],"Eulerian":[104],"large":[108],"order":[109],"with":[111,128],"minimum":[112,129],"degree":[113,130],"at":[114,131],"least":[115,132],"$0.91|V(G)|$":[116],"We":[121],"also":[122],"prove":[123],"$0.999|V(G)|$":[133],"$(1,4)$-choosable.":[137]},"counts_by_year":[{"year":2024,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}