{"id":"https://openalex.org/W4296917130","doi":"https://doi.org/10.1137/21m1432776","title":"The Overfullness of Graphs with Small Minimum Degree and Large Maximum Degree","display_name":"The Overfullness of Graphs with Small Minimum Degree and Large Maximum Degree","publication_year":2022,"publication_date":"2022-09-01","ids":{"openalex":"https://openalex.org/W4296917130","doi":"https://doi.org/10.1137/21m1432776"},"language":"en","primary_location":{"id":"doi:10.1137/21m1432776","is_oa":false,"landing_page_url":"https://doi.org/10.1137/21m1432776","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Discrete Mathematics","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/A5016568845","display_name":"Yan Cao","orcid":"https://orcid.org/0000-0002-9093-6034"},"institutions":[{"id":"https://openalex.org/I12097938","display_name":"West Virginia University","ror":"https://ror.org/011vxgd24","country_code":"US","type":"education","lineage":["https://openalex.org/I12097938"]},{"id":"https://openalex.org/I181565077","display_name":"Georgia State University","ror":"https://ror.org/03qt6ba18","country_code":"US","type":"education","lineage":["https://openalex.org/I181565077"]},{"id":"https://openalex.org/I25041050","display_name":"Augusta University","ror":"https://ror.org/012mef835","country_code":"US","type":"education","lineage":["https://openalex.org/I25041050"]},{"id":"https://openalex.org/I47301684","display_name":"Illinois State University","ror":"https://ror.org/050kcr883","country_code":"US","type":"education","lineage":["https://openalex.org/I47301684"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Yan Cao","raw_affiliation_strings":["Department of Mathematics, Illinois State Univeristy, Normal, IL 61790","Department of Mathematics, Augusta University, Augusta, GA 30912","Department of Mathematics, West Virginia University, Morgantown, WV 26506","Department of Mathematics and Statistics, Georgia State University, Atlanta, GA 30302"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Illinois State Univeristy, Normal, IL 61790","institution_ids":["https://openalex.org/I47301684"]},{"raw_affiliation_string":"Department of Mathematics, Augusta University, Augusta, GA 30912","institution_ids":["https://openalex.org/I25041050"]},{"raw_affiliation_string":"Department of Mathematics, West Virginia University, Morgantown, WV 26506","institution_ids":["https://openalex.org/I12097938"]},{"raw_affiliation_string":"Department of Mathematics and Statistics, Georgia State University, Atlanta, GA 30302","institution_ids":["https://openalex.org/I181565077"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5042737832","display_name":"Guantao Chen","orcid":"https://orcid.org/0000-0002-3118-6632"},"institutions":[{"id":"https://openalex.org/I12097938","display_name":"West Virginia University","ror":"https://ror.org/011vxgd24","country_code":"US","type":"education","lineage":["https://openalex.org/I12097938"]},{"id":"https://openalex.org/I181565077","display_name":"Georgia State University","ror":"https://ror.org/03qt6ba18","country_code":"US","type":"education","lineage":["https://openalex.org/I181565077"]},{"id":"https://openalex.org/I25041050","display_name":"Augusta University","ror":"https://ror.org/012mef835","country_code":"US","type":"education","lineage":["https://openalex.org/I25041050"]},{"id":"https://openalex.org/I47301684","display_name":"Illinois State University","ror":"https://ror.org/050kcr883","country_code":"US","type":"education","lineage":["https://openalex.org/I47301684"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Guantao Chen","raw_affiliation_strings":["Department of Mathematics, West Virginia University, Morgantown, WV 26506","Department of Mathematics and Statistics, Georgia State University, Atlanta, GA 30302","Department of Mathematics, Illinois State Univeristy, Normal, IL 61790","Department of Mathematics, Augusta University, Augusta, GA 30912"],"raw_orcid":"https://orcid.org/0000-0002-3118-6632","affiliations":[{"raw_affiliation_string":"Department of Mathematics, West Virginia University, Morgantown, WV 26506","institution_ids":["https://openalex.org/I12097938"]},{"raw_affiliation_string":"Department of Mathematics and Statistics, Georgia State University, Atlanta, GA 30302","institution_ids":["https://openalex.org/I181565077"]},{"raw_affiliation_string":"Department of Mathematics, Illinois State Univeristy, Normal, IL 61790","institution_ids":["https://openalex.org/I47301684"]},{"raw_affiliation_string":"Department of Mathematics, Augusta University, Augusta, GA 30912","institution_ids":["https://openalex.org/I25041050"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5018517775","display_name":"Guangming Jing","orcid":"https://orcid.org/0000-0003-0157-2687"},"institutions":[{"id":"https://openalex.org/I12097938","display_name":"West Virginia University","ror":"https://ror.org/011vxgd24","country_code":"US","type":"education","lineage":["https://openalex.org/I12097938"]},{"id":"https://openalex.org/I181565077","display_name":"Georgia State University","ror":"https://ror.org/03qt6ba18","country_code":"US","type":"education","lineage":["https://openalex.org/I181565077"]},{"id":"https://openalex.org/I25041050","display_name":"Augusta University","ror":"https://ror.org/012mef835","country_code":"US","type":"education","lineage":["https://openalex.org/I25041050"]},{"id":"https://openalex.org/I47301684","display_name":"Illinois State University","ror":"https://ror.org/050kcr883","country_code":"US","type":"education","lineage":["https://openalex.org/I47301684"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Guangming Jing","raw_affiliation_strings":["Department of Mathematics and Statistics, Georgia State University, Atlanta, GA 30302","Department of Mathematics, Augusta University, Augusta, GA 30912","Department of Mathematics, West Virginia University, Morgantown, WV 26506","Department of Mathematics, Illinois State Univeristy, Normal, IL 61790"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, Georgia State University, Atlanta, GA 30302","institution_ids":["https://openalex.org/I181565077"]},{"raw_affiliation_string":"Department of Mathematics, Augusta University, Augusta, GA 30912","institution_ids":["https://openalex.org/I25041050"]},{"raw_affiliation_string":"Department of Mathematics, West Virginia University, Morgantown, WV 26506","institution_ids":["https://openalex.org/I12097938"]},{"raw_affiliation_string":"Department of Mathematics, Illinois State Univeristy, Normal, IL 61790","institution_ids":["https://openalex.org/I47301684"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5015238599","display_name":"Songling Shan","orcid":"https://orcid.org/0000-0002-6384-2876"},"institutions":[{"id":"https://openalex.org/I12097938","display_name":"West Virginia University","ror":"https://ror.org/011vxgd24","country_code":"US","type":"education","lineage":["https://openalex.org/I12097938"]},{"id":"https://openalex.org/I181565077","display_name":"Georgia State University","ror":"https://ror.org/03qt6ba18","country_code":"US","type":"education","lineage":["https://openalex.org/I181565077"]},{"id":"https://openalex.org/I25041050","display_name":"Augusta University","ror":"https://ror.org/012mef835","country_code":"US","type":"education","lineage":["https://openalex.org/I25041050"]},{"id":"https://openalex.org/I47301684","display_name":"Illinois State University","ror":"https://ror.org/050kcr883","country_code":"US","type":"education","lineage":["https://openalex.org/I47301684"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Songling Shan","raw_affiliation_strings":["Department of Mathematics and Statistics, Georgia State University, Atlanta, GA 30302","Department of Mathematics, Illinois State Univeristy, Normal, IL 61790","Department of Mathematics, Augusta University, Augusta, GA 30912","Department of Mathematics, West Virginia University, Morgantown, WV 26506"],"raw_orcid":"https://orcid.org/0000-0002-6384-2876","affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, Georgia State University, Atlanta, GA 30302","institution_ids":["https://openalex.org/I181565077"]},{"raw_affiliation_string":"Department of Mathematics, Illinois State Univeristy, Normal, IL 61790","institution_ids":["https://openalex.org/I47301684"]},{"raw_affiliation_string":"Department of Mathematics, Augusta University, Augusta, GA 30912","institution_ids":["https://openalex.org/I25041050"]},{"raw_affiliation_string":"Department of Mathematics, West Virginia University, Morgantown, WV 26506","institution_ids":["https://openalex.org/I12097938"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.14561479,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"36","issue":"3","first_page":"2258","last_page":"2270"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9997000098228455,"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/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9980999827384949,"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":0.8995407223701477},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8260299563407898},{"id":"https://openalex.org/keywords/delta","display_name":"Delta","score":0.7126028537750244},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.6319559216499329},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.6034321188926697},{"id":"https://openalex.org/keywords/simple-graph","display_name":"Simple graph","score":0.5897735953330994},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5199400186538696},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.44163960218429565},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.08939099311828613}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8995407223701477},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8260299563407898},{"id":"https://openalex.org/C5072461","wikidata":"https://www.wikidata.org/wiki/Q49506","display_name":"Delta","level":2,"score":0.7126028537750244},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.6319559216499329},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.6034321188926697},{"id":"https://openalex.org/C2993105083","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Simple graph","level":3,"score":0.5897735953330994},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5199400186538696},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.44163960218429565},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08939099311828613},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C1276947","wikidata":"https://www.wikidata.org/wiki/Q333","display_name":"Astronomy","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/21m1432776","is_oa":false,"landing_page_url":"https://doi.org/10.1137/21m1432776","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Discrete Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2353173197","display_name":"Density and Edge Coloring","funder_award_id":"2001130","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G3395733139","display_name":"Edge Coloring and Edge Cover Packing","funder_award_id":"1855716","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7195926418","display_name":null,"funder_award_id":"DMS-1855716","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7769902126","display_name":null,"funder_award_id":"DMS-2001130","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":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":10,"referenced_works":["https://openalex.org/W655585282","https://openalex.org/W1493850023","https://openalex.org/W1504246017","https://openalex.org/W2059233598","https://openalex.org/W2102669784","https://openalex.org/W2151370292","https://openalex.org/W2603101721","https://openalex.org/W4214875510","https://openalex.org/W4220797201","https://openalex.org/W4250807908"],"related_works":["https://openalex.org/W2951305269","https://openalex.org/W2897806428","https://openalex.org/W2391518723","https://openalex.org/W3206431649","https://openalex.org/W2010965931","https://openalex.org/W2805115653","https://openalex.org/W1996149838","https://openalex.org/W3014749936","https://openalex.org/W4205475737","https://openalex.org/W2364012696"],"abstract_inverted_index":{"Given":[0],"a":[1,51,79],"simple":[2],"graph":[3,108],"$G$,":[4,22,40],"denote":[5],"by":[6],"$\\Delta(G)$,":[7],"$\\delta(G)$,":[8],"and":[9,17,31,41,89],"$\\chi'(G)$":[10],"the":[11,14,18],"maximum":[12,52],"degree,":[13,16],"minimum":[15],"chromatic":[19],"index":[20],"of":[21,39,87],"respectively.":[23],"We":[24],"say":[25],"$G$":[26,42,55,72,77,93,109],"is":[27,43,73,94,110],"$\\Delta$-critical":[28,80,107],"if":[29,45,71,112],"$\\chi'(G)=\\Delta(G)+1$":[30],"$\\chi'(H)\\le":[32],"\\Delta(G)$":[33],"for":[34],"every":[35],"proper":[36],"subgraph":[37],"$H$":[38],"overfull":[44,85,95,111],"$|E(G)|>\\Delta(G)":[46],"\\lfloor":[47],"|V(G)|/2":[48,62],"\\rfloor$.":[49],"Since":[50],"matching":[53],"in":[54],"can":[56],"have":[57],"size":[58],"at":[59],"most":[60],"$\\lfloor":[61],"\\rfloor$,":[63],"it":[64],"follows":[65],"that":[66,92,105],"$\\chi'(G)":[67],"=":[68],"\\Delta(G)":[69],"+1$":[70],"overfull.":[74],"Conversely,":[75],"let":[76],"be":[78],"graph.":[81],"The":[82],"well":[83],"known":[84],"conjecture":[86],"Chetwynd":[88],"Hilton":[90],"asserts":[91],"provided":[96],"$\\Delta(G)":[97,113],">":[98],"|V(G)|/3$.":[99],"In":[100],"this":[101],"paper,":[102],"we":[103],"show":[104],"any":[106],"-":[114],"7\\delta(G)/4\\ge":[115],"(3|V(G)|-17)/4$.":[116]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
