{"id":"https://openalex.org/W2139499792","doi":"https://doi.org/10.37236/1585","title":"All Regular Multigraphs of Even Order and High Degree Are 1-factorable","display_name":"All Regular Multigraphs of Even Order and High Degree Are 1-factorable","publication_year":2001,"publication_date":"2001-12-08","ids":{"openalex":"https://openalex.org/W2139499792","doi":"https://doi.org/10.37236/1585","mag":"2139499792"},"language":"en","primary_location":{"id":"doi:10.37236/1585","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1585","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v8i1r41/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":false,"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":null,"license_id":null,"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":"bronze","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v8i1r41/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5051665245","display_name":"Michael J. Plantholt","orcid":"https://orcid.org/0000-0001-8956-0626"},"institutions":[{"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":true,"raw_author_name":"Michael J. Plantholt","raw_affiliation_strings":["Department of Mathematics Illinois State University Normal, IL 61790-4520, USA","Illinois State University,"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics Illinois State University Normal, IL 61790-4520, USA","institution_ids":["https://openalex.org/I47301684"]},{"raw_affiliation_string":"Illinois State University,","institution_ids":["https://openalex.org/I47301684"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5054487178","display_name":"Shailesh K. Tipnis","orcid":null},"institutions":[{"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":"Shailesh K. Tipnis","raw_affiliation_strings":["Department of Mathematics Illinois State University Normal, IL 61790-4520, USA","Illinois State University,"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics Illinois State University Normal, IL 61790-4520, USA","institution_ids":["https://openalex.org/I47301684"]},{"raw_affiliation_string":"Illinois State University,","institution_ids":["https://openalex.org/I47301684"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5051665245"],"corresponding_institution_ids":["https://openalex.org/I47301684"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":12,"citation_normalized_percentile":{"value":0.23829787,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"8","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":0.9998000264167786,"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":0.9998000264167786,"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/T11797","display_name":"graph theory and CDMA systems","score":0.9945999979972839,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10849","display_name":"Finite Group Theory Research","score":0.9940999746322632,"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/mathematics","display_name":"Mathematics","score":0.8965153694152832},{"id":"https://openalex.org/keywords/multigraph","display_name":"Multigraph","score":0.8900501132011414},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8359016180038452},{"id":"https://openalex.org/keywords/multiplicity","display_name":"Multiplicity (mathematics)","score":0.7109944820404053},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.6623678803443909},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.6508786678314209},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.6296869516372681},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.5455408096313477},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.4965212941169739},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.44759589433670044},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4402104914188385},{"id":"https://openalex.org/keywords/factorization","display_name":"Factorization","score":0.43704646825790405},{"id":"https://openalex.org/keywords/simple-graph","display_name":"Simple graph","score":0.41550761461257935},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.051337629556655884}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8965153694152832},{"id":"https://openalex.org/C17758045","wikidata":"https://www.wikidata.org/wiki/Q2642629","display_name":"Multigraph","level":3,"score":0.8900501132011414},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8359016180038452},{"id":"https://openalex.org/C156004811","wikidata":"https://www.wikidata.org/wiki/Q2228257","display_name":"Multiplicity (mathematics)","level":2,"score":0.7109944820404053},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.6623678803443909},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.6508786678314209},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.6296869516372681},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.5455408096313477},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.4965212941169739},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.44759589433670044},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4402104914188385},{"id":"https://openalex.org/C187834632","wikidata":"https://www.wikidata.org/wiki/Q188804","display_name":"Factorization","level":2,"score":0.43704646825790405},{"id":"https://openalex.org/C2993105083","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Simple graph","level":3,"score":0.41550761461257935},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.051337629556655884},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","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},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.37236/1585","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1585","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v8i1r41/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":false,"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.7.7927","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.7.7927","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.combinatorics.org/Volume_8/PostScriptfiles/v8i1r41.ps","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.8.7548","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.8.7548","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.combinatorics.org/Volume_8/PDF/v8i1r41.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.37236/1585","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1585","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v8i1r41/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":false,"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":null,"license_id":null,"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":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2139499792.pdf","grobid_xml":"https://content.openalex.org/works/W2139499792.grobid-xml"},"referenced_works_count":10,"referenced_works":["https://openalex.org/W1484040084","https://openalex.org/W1510730180","https://openalex.org/W1971367602","https://openalex.org/W1986598403","https://openalex.org/W1986604231","https://openalex.org/W2048300035","https://openalex.org/W2085379850","https://openalex.org/W2317309498","https://openalex.org/W4251288793","https://openalex.org/W4300303686"],"related_works":["https://openalex.org/W2365751441","https://openalex.org/W1988736474","https://openalex.org/W2024593554","https://openalex.org/W2298713664","https://openalex.org/W4322716708","https://openalex.org/W4306653310","https://openalex.org/W2063149200","https://openalex.org/W4243103456","https://openalex.org/W2065218154","https://openalex.org/W2964243625"],"abstract_inverted_index":{"Plantholt":[0],"and":[1,23,29,49,51],"Tipnis":[2],"(1991)":[3],"proved":[4,54],"that":[5,55],"for":[6,59],"any":[7,45],"even":[8,16],"integer":[9],"$r$,":[10],"a":[11,78],"regular":[12],"multigraph":[13],"$G$":[14],"with":[15],"order":[17],"$n$,":[18],"multiplicity":[19],"$\\mu(G)":[20],"\\leq":[21],"r$":[22],"degree":[24],"high":[25],"relative":[26],"to":[27,38,77],"$n$":[28],"$r$":[30,43],"is":[31,44,62],"1-factorable.":[32],"Here":[33],"we":[34],"extend":[35],"this":[36,71],"result":[37,73,81],"include":[39],"the":[40,56],"case":[41],"when":[42],"odd":[46],"integer.":[47],"H\u00e4ggkvist":[48],"Perkovi\u0107":[50],"Reed":[52],"(1997)":[53],"One-factorization":[57],"Conjecture":[58],"simple":[60,75],"graphs":[61,76],"asymptotically":[63],"true.":[64],"Our":[65],"techniques":[66],"yield":[67],"an":[68],"extension":[69],"of":[70],"asymptotic":[72,80],"on":[74,82],"corresponding":[79],"multigraphs.":[83]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-11T06:13:24.991567","created_date":"2025-10-10T00:00:00"}