{"id":"https://openalex.org/W7131677390","doi":"https://doi.org/10.37236/13620","title":"Coloring Locally Sparse Graphs","display_name":"Coloring Locally Sparse Graphs","publication_year":2026,"publication_date":"2026-02-13","ids":{"openalex":"https://openalex.org/W7131677390","doi":"https://doi.org/10.37236/13620"},"language":null,"primary_location":{"id":"doi:10.37236/13620","is_oa":true,"landing_page_url":"https://doi.org/10.37236/13620","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v33i1p31/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/v33i1p31/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5126907848","display_name":"James Anderson","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"James Anderson","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5126885651","display_name":"Abhishek Dhawan","orcid":null},"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":false,"raw_author_name":"Abhishek Dhawan","raw_affiliation_strings":["University of Illinois at Urbana-Champaign"],"affiliations":[{"raw_affiliation_string":"University of Illinois at Urbana-Champaign","institution_ids":["https://openalex.org/I157725225"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5094077635","display_name":"Aiya Kuchukova","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Aiya Kuchukova","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5126907848"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.5378198,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"33","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11329","display_name":"Limits and Structures in Graph Theory","score":0.5353000164031982,"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"}},"topics":[{"id":"https://openalex.org/T11329","display_name":"Limits and Structures in Graph Theory","score":0.5353000164031982,"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"}},{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.4090000092983246,"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":0.017400000244379044,"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/bipartite-graph","display_name":"Bipartite graph","score":0.6139000058174133},{"id":"https://openalex.org/keywords/graph-factorization","display_name":"Graph factorization","score":0.45750001072883606},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.44690001010894775},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4415000081062317},{"id":"https://openalex.org/keywords/induced-subgraph","display_name":"Induced subgraph","score":0.43309998512268066},{"id":"https://openalex.org/keywords/cograph","display_name":"Cograph","score":0.39590001106262207},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.37549999356269836},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.37290000915527344},{"id":"https://openalex.org/keywords/complete-bipartite-graph","display_name":"Complete bipartite graph","score":0.3603000044822693}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.775600016117096},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6697999835014343},{"id":"https://openalex.org/C197657726","wikidata":"https://www.wikidata.org/wiki/Q174733","display_name":"Bipartite graph","level":3,"score":0.6139000058174133},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5110999941825867},{"id":"https://openalex.org/C128115575","wikidata":"https://www.wikidata.org/wiki/Q5597083","display_name":"Graph factorization","level":5,"score":0.45750001072883606},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.44690001010894775},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4415000081062317},{"id":"https://openalex.org/C2778012994","wikidata":"https://www.wikidata.org/wiki/Q24743362","display_name":"Induced subgraph","level":4,"score":0.43309998512268066},{"id":"https://openalex.org/C59824394","wikidata":"https://www.wikidata.org/wiki/Q5141281","display_name":"Cograph","level":5,"score":0.39590001106262207},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.37549999356269836},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.37290000915527344},{"id":"https://openalex.org/C134119311","wikidata":"https://www.wikidata.org/wiki/Q913598","display_name":"Complete bipartite graph","level":4,"score":0.3603000044822693},{"id":"https://openalex.org/C147792647","wikidata":"https://www.wikidata.org/wiki/Q5282847","display_name":"Distance-hereditary graph","level":5,"score":0.3573000133037567},{"id":"https://openalex.org/C76946457","wikidata":"https://www.wikidata.org/wiki/Q504843","display_name":"Graph coloring","level":3,"score":0.33570000529289246},{"id":"https://openalex.org/C158319403","wikidata":"https://www.wikidata.org/wiki/Q5477527","display_name":"Fractional coloring","level":5,"score":0.32919999957084656},{"id":"https://openalex.org/C13251829","wikidata":"https://www.wikidata.org/wiki/Q3085841","display_name":"Dense graph","level":5,"score":0.31610000133514404},{"id":"https://openalex.org/C123809776","wikidata":"https://www.wikidata.org/wiki/Q1050972","display_name":"Edge coloring","level":5,"score":0.302700012922287},{"id":"https://openalex.org/C36038622","wikidata":"https://www.wikidata.org/wiki/Q5428703","display_name":"Factor-critical graph","level":5,"score":0.3005000054836273},{"id":"https://openalex.org/C64339825","wikidata":"https://www.wikidata.org/wiki/Q722659","display_name":"Graph property","level":5,"score":0.2922999858856201},{"id":"https://openalex.org/C149530733","wikidata":"https://www.wikidata.org/wiki/Q5597091","display_name":"Graph power","level":4,"score":0.2897999882698059},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.28529998660087585},{"id":"https://openalex.org/C38767284","wikidata":"https://www.wikidata.org/wiki/Q5601715","display_name":"Greedy coloring","level":5,"score":0.27000001072883606},{"id":"https://openalex.org/C199594403","wikidata":"https://www.wikidata.org/wiki/Q1130404","display_name":"List coloring","level":5,"score":0.26919999718666077},{"id":"https://openalex.org/C8554925","wikidata":"https://www.wikidata.org/wiki/Q3893853","display_name":"Split graph","level":5,"score":0.2623000144958496},{"id":"https://openalex.org/C43413943","wikidata":"https://www.wikidata.org/wiki/Q4927193","display_name":"Block graph","level":5,"score":0.25060001015663147}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.37236/13620","is_oa":true,"landing_page_url":"https://doi.org/10.37236/13620","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v33i1p31/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:10.37236/13620","is_oa":true,"landing_page_url":"https://doi.org/10.37236/13620","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v33i1p31/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":[{"id":"https://metadata.un.org/sdg/11","display_name":"Sustainable cities and communities","score":0.4397980570793152}],"awards":[{"id":"https://openalex.org/G154586071","display_name":null,"funder_award_id":"DMS-1937241","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G2754861783","display_name":null,"funder_award_id":"2239187","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G2914511613","display_name":"Learning Combinatorial Non-Convex Structures in Data: Statistical Foundations and Computational Methods","funder_award_id":"2053333","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6266717420","display_name":null,"funder_award_id":"DMS-2053333","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6671297155","display_name":null,"funder_award_id":"CAREER","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6894402473","display_name":null,"funder_award_id":"Fellowship","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G848032724","display_name":null,"funder_award_id":"Science","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W7131677390.pdf"},"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"A":[0],"graph":[1,36,68,109],"$G$":[2,37,61,112,153],"is":[3,42,113,139,154],"$k$-locally":[4],"sparse":[5],"if":[6,34,70,111],"for":[7,30,66,71,106,158,164],"each":[8,72],"vertex":[9,73],"$v":[10,74],"\\in":[11,75],"V(G)$,":[12],"the":[13,77,81,93,99,103,135,146,170],"subgraph":[14,78],"induced":[15,79],"by":[16,58,80],"its":[17],"neighborhood":[18,82],"contains":[19,85],"at":[20,86],"most":[21,87],"$k$":[22,88],"edges.":[23],"Alon,":[24],"Krivelevich,":[25],"and":[26,131,162,166],"Sudakov":[27],"showed":[28],"that":[29],"$f":[31],">":[32],"0$":[33],"a":[35,51,140],"of":[38,55,83,90,102,127],"maximum":[39],"degree":[40],"$\\Delta$":[41],"$\\Delta^2/f$-locally-sparse,":[43],"then":[44,116],"$\\chi(G)":[45,117],"=":[46,118],"O\\left(\\Delta/\\log":[47],"f\\right)$.":[48],"We":[49],"introduce":[50],"more":[52,171],"general":[53,172],"notion":[54],"local":[56],"sparsity":[57],"defining":[59],"graphs":[60],"to":[62],"be":[63],"$(k,":[64,114],"F)$-locally-sparse":[65],"some":[67],"$F$":[69,138],"V(G)$":[76],"$v$":[84],"copies":[89],"$F$.":[91],"Employing":[92],"R\u00f6dl":[94],"nibble":[95],"method,":[96],"we":[97],"prove":[98],"following":[100],"generalization":[101],"above":[104],"result:":[105],"every":[107],"bipartite":[108],"$F$,":[110],"F)$-locally-sparse,":[115],"O\\left(":[119],"\\Delta":[120],"/\\log\\left(\\Delta":[121],"k^{-1/|V(F)|}\\right)\\right)$.":[122],"This":[123],"improves":[124],"upon":[125],"results":[126,143],"Davies,":[128],"Kang,":[129],"Pirot,":[130],"Sereni":[132],"who":[133],"consider":[134],"case":[136],"when":[137,152],"path.":[141],"Our":[142],"also":[144],"recover":[145],"best":[147],"known":[148],"bound":[149],"on":[150],"$\\chi(G)$":[151],"$K_{1,":[155],"t,":[156],"t}$-free":[157],"$t":[159],"\\geq":[160],"4$,":[161],"hold":[163],"list":[165],"correspondence":[167],"coloring":[168],"in":[169],"so-called":[173],"\"color-degree\"":[174],"setting.":[175]},"counts_by_year":[],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2026-02-27T00:00:00"}