{"id":"https://openalex.org/W2727246442","doi":"https://doi.org/10.1142/s1793830917500471","title":"The linear 2-arboricity of sparse graphs","display_name":"The linear 2-arboricity of sparse graphs","publication_year":2017,"publication_date":"2017-07-03","ids":{"openalex":"https://openalex.org/W2727246442","doi":"https://doi.org/10.1142/s1793830917500471","mag":"2727246442"},"language":"en","primary_location":{"id":"doi:10.1142/s1793830917500471","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s1793830917500471","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/A5077749078","display_name":"Yuanchao Li","orcid":"https://orcid.org/0000-0002-8005-947X"},"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":true,"raw_author_name":"Yuanchao Li","raw_affiliation_strings":["Department of Mathematics, Zhejiang Normal University, Jinhua 321004, P. R. China"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Zhejiang Normal University, Jinhua 321004, P. R. China","institution_ids":["https://openalex.org/I135237710"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5016166995","display_name":"Xiaoxue Hu","orcid":"https://orcid.org/0000-0001-7848-6870"},"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":"Xiaoxue Hu","raw_affiliation_strings":["Department of Mathematics, Zhejiang Normal University, Jinhua 321004, P. R. China"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Zhejiang Normal University, Jinhua 321004, P. R. China","institution_ids":["https://openalex.org/I135237710"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5077749078"],"corresponding_institution_ids":["https://openalex.org/I135237710"],"apc_list":null,"apc_paid":null,"fwci":0.4542,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.64877169,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"09","issue":"04","first_page":"1750047","last_page":"1750047"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9995999932289124,"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":0.9995999932289124,"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":0.9930999875068665,"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/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.984000027179718,"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/arboricity","display_name":"Arboricity","score":0.9425750374794006},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6951626539230347},{"id":"https://openalex.org/keywords/disjoint-sets","display_name":"Disjoint sets","score":0.6168997883796692},{"id":"https://openalex.org/keywords/dense-graph","display_name":"Dense graph","score":0.6115099787712097},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5849303007125854},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5507529377937317},{"id":"https://openalex.org/keywords/degenerate-energy-levels","display_name":"Degenerate energy levels","score":0.4299652576446533},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3531162142753601},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.1741393804550171},{"id":"https://openalex.org/keywords/1-planar-graph","display_name":"1-planar graph","score":0.15453356504440308},{"id":"https://openalex.org/keywords/planar-graph","display_name":"Planar graph","score":0.13685590028762817},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1273970901966095}],"concepts":[{"id":"https://openalex.org/C83204008","wikidata":"https://www.wikidata.org/wiki/Q4784907","display_name":"Arboricity","level":4,"score":0.9425750374794006},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6951626539230347},{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.6168997883796692},{"id":"https://openalex.org/C13251829","wikidata":"https://www.wikidata.org/wiki/Q3085841","display_name":"Dense graph","level":5,"score":0.6115099787712097},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5849303007125854},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5507529377937317},{"id":"https://openalex.org/C72319582","wikidata":"https://www.wikidata.org/wiki/Q584304","display_name":"Degenerate energy levels","level":2,"score":0.4299652576446533},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3531162142753601},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.1741393804550171},{"id":"https://openalex.org/C102192266","wikidata":"https://www.wikidata.org/wiki/Q4545823","display_name":"1-planar graph","level":4,"score":0.15453356504440308},{"id":"https://openalex.org/C101837359","wikidata":"https://www.wikidata.org/wiki/Q547823","display_name":"Planar graph","level":3,"score":0.13685590028762817},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1273970901966095},{"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:10.1142/s1793830917500471","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s1793830917500471","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":[{"display_name":"Life in Land","id":"https://metadata.un.org/sdg/15","score":0.6700000166893005}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W25916205","https://openalex.org/W104959759","https://openalex.org/W1483404362","https://openalex.org/W1640262016","https://openalex.org/W1871888924","https://openalex.org/W2003295666","https://openalex.org/W2039274034","https://openalex.org/W2042182786","https://openalex.org/W2046587597","https://openalex.org/W2051937400","https://openalex.org/W2088603101","https://openalex.org/W2090014838","https://openalex.org/W2363074029","https://openalex.org/W2536844146","https://openalex.org/W2751085793","https://openalex.org/W2751135937","https://openalex.org/W3150924206","https://openalex.org/W4246719015"],"related_works":["https://openalex.org/W2950893338","https://openalex.org/W4289666645","https://openalex.org/W2886745396","https://openalex.org/W2962805102","https://openalex.org/W3011393812","https://openalex.org/W4298370844","https://openalex.org/W3012533071","https://openalex.org/W2128081519","https://openalex.org/W2032688631","https://openalex.org/W2007680378"],"abstract_inverted_index":{"The":[0],"linear":[1,50],"[Formula:":[2,5,11,18,23,30,51,64,73,78,82,87,91,96,100,105,109],"see":[3,6,12,19,24,31,52,65,74,79,83,88,92,97,101,106,110],"text]-arboricity":[4,53],"text]":[7,13,20,25,32,66],"of":[8,39,54],"a":[9,68],"graph":[10],"is":[14],"the":[15,49,59],"least":[16],"integer":[17],"such":[21],"that":[22],"can":[26],"be":[27,67],"partitioned":[28],"into":[29],"edge-disjoint":[33],"forests,":[34],"whose":[35],"components":[36],"are":[37],"paths":[38],"length":[40],"at":[41],"most":[42],"2.":[43],"In":[44],"this":[45],"paper,":[46],"we":[47,71],"study":[48],"sparse":[55],"graphs,":[56],"and":[57],"prove":[58],"following":[60],"results:":[61],"(1)":[62],"let":[63],"2-degenerate":[69],"graph,":[70],"have":[72],"text];":[75,84,93,102],"(2)":[76],"if":[77,86,95,104],"text],":[80,89,98,107],"then":[81,90,99,108],"(3)":[85],"(4)":[94],"(5)":[103],"text].":[111]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}