{"id":"https://openalex.org/W4387770844","doi":"https://doi.org/10.37236/11774","title":"Weak (2,3)-Decomposition of Planar Graphs","display_name":"Weak (2,3)-Decomposition of Planar Graphs","publication_year":2023,"publication_date":"2023-10-19","ids":{"openalex":"https://openalex.org/W4387770844","doi":"https://doi.org/10.37236/11774"},"language":"en","primary_location":{"id":"doi:10.37236/11774","is_oa":true,"landing_page_url":"http://dx.doi.org/10.37236/11774","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v30i4p14/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/v30i4p14/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101719301","display_name":"Ming Han","orcid":"https://orcid.org/0000-0002-1639-5209"},"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":"Ming Han","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":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.20646477,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"30","issue":"4","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":0.965399980545044,"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":0.965399980545044,"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":0.8808871507644653},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8071020245552063},{"id":"https://openalex.org/keywords/planar-graph","display_name":"Planar graph","score":0.6757252812385559},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5647838115692139},{"id":"https://openalex.org/keywords/partition","display_name":"Partition (number theory)","score":0.5622384548187256},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.5088401436805725},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.38119256496429443}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8808871507644653},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8071020245552063},{"id":"https://openalex.org/C101837359","wikidata":"https://www.wikidata.org/wiki/Q547823","display_name":"Planar graph","level":3,"score":0.6757252812385559},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5647838115692139},{"id":"https://openalex.org/C42812","wikidata":"https://www.wikidata.org/wiki/Q1082910","display_name":"Partition (number theory)","level":2,"score":0.5622384548187256},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.5088401436805725},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.38119256496429443}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.37236/11774","is_oa":true,"landing_page_url":"http://dx.doi.org/10.37236/11774","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v30i4p14/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:10.37236/11774","is_oa":true,"landing_page_url":"http://dx.doi.org/10.37236/11774","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v30i4p14/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":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4387770844.pdf"},"referenced_works_count":11,"referenced_works":["https://openalex.org/W264180933","https://openalex.org/W2009827511","https://openalex.org/W2093490044","https://openalex.org/W2145878357","https://openalex.org/W2624651727","https://openalex.org/W2903133977","https://openalex.org/W2962706353","https://openalex.org/W3009314871","https://openalex.org/W3040336391","https://openalex.org/W6627695045","https://openalex.org/W6739321967"],"related_works":["https://openalex.org/W2267059662","https://openalex.org/W4388411807","https://openalex.org/W2364268683","https://openalex.org/W2478803962","https://openalex.org/W2144570076","https://openalex.org/W3169430512","https://openalex.org/W1606013690","https://openalex.org/W4293743430","https://openalex.org/W3006156235","https://openalex.org/W2073591271"],"abstract_inverted_index":{"This":[0,84],"paper":[1],"introduces":[2],"the":[3,86],"concept":[4],"of":[5,8,18,76,82,100],"weak":[6,54],"$(d,h)$-decomposition":[7],"a":[9,16,28,35,53,57,64,79],"graph":[10,30,51,61,111],"$G$,":[11],"which":[12],"is":[13,70,78,112],"defined":[14],"as":[15],"partition":[17],"$E(G)$":[19],"into":[20],"two":[21],"subsets":[22],"$E_1,E_2$,":[23],"such":[24,67],"that":[25,48,68,108],"$E_1$":[26],"induces":[27,34],"$d$-degenerate":[29],"$H_1$":[31],"and":[32,72,95],"$E_2$":[33],"subgraph":[36,65],"$H_2$":[37],"with":[38],"$\\alpha(H_1[N_{H_2}(v)])":[39],"\\le":[40],"h$":[41],"for":[42],"any":[43,73],"vertex":[44],"$v$.":[45],"We":[46],"prove":[47],"each":[49],"planar":[50,60,101,110],"admits":[52],"$(2,3)$-decomposition.":[55],"As":[56],"consequence,":[58],"every":[59,109],"$G$":[62],"has":[63],"$H$":[66],"$G-E(H)$":[69,77],"$3$-paintable":[71],"proper":[74],"coloring":[75,81],"$3$-defective":[80],"$G$.":[83],"improves":[85],"result":[87],"in":[88],"[G.":[89],"Gutowski,":[90],"M.":[91],"Han,":[92],"T.":[93],"Krawczyk,":[94],"X.":[96],"Zhu,":[97],"Defective":[98],"$3$-paintability":[99],"graphs,":[102],"Electron.":[103],"J.":[104],"Combin.,":[105],"25(2):\\#P2.34,":[106],"2018]":[107],"3-defective":[113],"$3$-paintable.":[114]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}