{"id":"https://openalex.org/W1947524870","doi":"https://doi.org/10.37236/3876","title":"Characterization of $(2m,m)$-Paintable Graphs","display_name":"Characterization of $(2m,m)$-Paintable Graphs","publication_year":2015,"publication_date":"2015-04-29","ids":{"openalex":"https://openalex.org/W1947524870","doi":"https://doi.org/10.37236/3876","mag":"1947524870"},"language":"en","primary_location":{"id":"doi:10.37236/3876","is_oa":true,"landing_page_url":"https://doi.org/10.37236/3876","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v22i2p14/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/v22i2p14/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5073136526","display_name":"Thomas A. Mahoney","orcid":"https://orcid.org/0000-0002-7401-8727"},"institutions":[{"id":"https://openalex.org/I157725225","display_name":"University of Illinois Urbana-Champaign","ror":"https://ror.org/047426m28","country_code":"US","type":"education","lineage":["https://openalex.org/I157725225"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Thomas Mahoney","raw_affiliation_strings":["University of Illinois at Urbana-Champaign","University of Illinois at Urbana Champaign"],"affiliations":[{"raw_affiliation_string":"University of Illinois at Urbana-Champaign","institution_ids":["https://openalex.org/I157725225"]},{"raw_affiliation_string":"University of Illinois at Urbana Champaign","institution_ids":["https://openalex.org/I157725225"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5002679592","display_name":"Jixian Meng","orcid":null},"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":"Jixian Meng","raw_affiliation_strings":["Zhejiang Normal University"],"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"],"affiliations":[{"raw_affiliation_string":"Zhejiang Normal University","institution_ids":["https://openalex.org/I135237710"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5073136526"],"corresponding_institution_ids":["https://openalex.org/I157725225"],"apc_list":null,"apc_paid":null,"fwci":0.3639,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.64518558,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"22","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":0.9998000264167786,"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":0.9998000264167786,"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":0.9988999962806702,"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9907000064849854,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8347024917602539},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8115226030349731},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.6573225259780884},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5599732398986816},{"id":"https://openalex.org/keywords/characterization","display_name":"Characterization (materials science)","score":0.5052860379219055},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.42778280377388},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.07067087292671204},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.03688880801200867}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8347024917602539},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8115226030349731},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.6573225259780884},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5599732398986816},{"id":"https://openalex.org/C2780841128","wikidata":"https://www.wikidata.org/wiki/Q5073781","display_name":"Characterization (materials science)","level":2,"score":0.5052860379219055},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.42778280377388},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.07067087292671204},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.03688880801200867},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.37236/3876","is_oa":true,"landing_page_url":"https://doi.org/10.37236/3876","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v22i2p14/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:10.37236/3876","is_oa":true,"landing_page_url":"https://doi.org/10.37236/3876","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v22i2p14/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/G36348540","display_name":null,"funder_award_id":"11171310","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5848258319","display_name":null,"funder_award_id":"0 and","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320338464","display_name":"Natural Science Foundation of Zhejiang Province","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1947524870.pdf","grobid_xml":"https://content.openalex.org/works/W1947524870.grobid-xml"},"referenced_works_count":7,"referenced_works":["https://openalex.org/W1587621605","https://openalex.org/W1598828859","https://openalex.org/W1838245566","https://openalex.org/W2015381291","https://openalex.org/W2055085175","https://openalex.org/W2055859399","https://openalex.org/W2156678756"],"related_works":["https://openalex.org/W3107994849","https://openalex.org/W4247143848","https://openalex.org/W2735573198","https://openalex.org/W2009883749","https://openalex.org/W29442446","https://openalex.org/W2896904446","https://openalex.org/W330727063","https://openalex.org/W1483407203","https://openalex.org/W4206825956","https://openalex.org/W2027794350"],"abstract_inverted_index":{"In":[0],"this":[1,45],"paper,":[2],"we":[3],"prove":[4],"that":[5],"for":[6,37,50],"any":[7,11,38],"graph":[8],"$G$":[9,15,22],"and":[10,19],"positive":[12,39],"integer":[13,40],"$m$,":[14],"is":[16,23],"$(2m,m)$-paintable":[17],"if":[18,21],"only":[20],"2-paintable.":[24],"It":[25],"was":[26],"asked":[27],"by":[28],"Zhu":[29],"in":[30,47],"2009":[31],"whether":[32],"$k$-paintable":[33],"graphs":[34],"are":[35],"$(km,m)$-paintable":[36],"$m$.":[41],"Our":[42],"result":[43],"answers":[44],"question":[46],"the":[48],"affirmative":[49],"$k=2$.":[51]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2015,"cited_by_count":1}],"updated_date":"2026-04-13T07:58:08.660418","created_date":"2025-10-10T00:00:00"}
