{"id":"https://openalex.org/W3198523402","doi":"https://doi.org/10.37236/10988","title":"Betwixt and Between 2-Factor Hamiltonian and Perfect-Matching-Hamiltonian Graphs","display_name":"Betwixt and Between 2-Factor Hamiltonian and Perfect-Matching-Hamiltonian Graphs","publication_year":2023,"publication_date":"2023-04-07","ids":{"openalex":"https://openalex.org/W3198523402","doi":"https://doi.org/10.37236/10988","mag":"3198523402"},"language":"en","primary_location":{"id":"doi:10.37236/10988","is_oa":true,"landing_page_url":"https://doi.org/10.37236/10988","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v30i2p5/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":"preprint","indexed_in":["arxiv","crossref","datacite","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v30i2p5/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5029393897","display_name":"Federico Romaniello","orcid":null},"institutions":[{"id":"https://openalex.org/I20272500","display_name":"University of Basilicata","ror":"https://ror.org/03tc05689","country_code":"IT","type":"education","lineage":["https://openalex.org/I20272500"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Federico Romaniello","raw_affiliation_strings":["Dipartimento di Matematica, Informatica ed Economia, Universit\u00e0 degli Studi della Basilicata","University of Basilicata"],"affiliations":[{"raw_affiliation_string":"Dipartimento di Matematica, Informatica ed Economia, Universit\u00e0 degli Studi della Basilicata","institution_ids":["https://openalex.org/I20272500"]},{"raw_affiliation_string":"University of Basilicata","institution_ids":["https://openalex.org/I20272500"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5025609803","display_name":"Jean Paul Zerafa","orcid":"https://orcid.org/0000-0002-3159-2980"},"institutions":[{"id":"https://openalex.org/I74788687","display_name":"Comenius University Bratislava","ror":"https://ror.org/0587ef340","country_code":"SK","type":"education","lineage":["https://openalex.org/I74788687"]}],"countries":["SK"],"is_corresponding":false,"raw_author_name":"Jean Paul Zerafa","raw_affiliation_strings":["Comenius University Bratislava"],"affiliations":[{"raw_affiliation_string":"Comenius University Bratislava","institution_ids":["https://openalex.org/I74788687"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5029393897"],"corresponding_institution_ids":["https://openalex.org/I20272500"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.00113355,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"30","issue":"2","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.9988999962806702,"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"}},"topics":[{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.9988999962806702,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9986000061035156,"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/T10849","display_name":"Finite Group Theory Research","score":0.9879000186920166,"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":0.7960339784622192},{"id":"https://openalex.org/keywords/foster-graph","display_name":"Foster graph","score":0.693092942237854},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6842978000640869},{"id":"https://openalex.org/keywords/bipartite-graph","display_name":"Bipartite graph","score":0.6309505701065063},{"id":"https://openalex.org/keywords/quartic-graph","display_name":"Quartic graph","score":0.5741574168205261},{"id":"https://openalex.org/keywords/cubic-graph","display_name":"Cubic graph","score":0.5736172795295715},{"id":"https://openalex.org/keywords/complete-bipartite-graph","display_name":"Complete bipartite graph","score":0.5096001625061035},{"id":"https://openalex.org/keywords/edge-transitive-graph","display_name":"Edge-transitive graph","score":0.5067928433418274},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4959810674190521},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.4906529486179352},{"id":"https://openalex.org/keywords/factor-critical-graph","display_name":"Factor-critical graph","score":0.4850398898124695},{"id":"https://openalex.org/keywords/pancyclic-graph","display_name":"Pancyclic graph","score":0.46940314769744873},{"id":"https://openalex.org/keywords/voltage-graph","display_name":"Voltage graph","score":0.4351625442504883},{"id":"https://openalex.org/keywords/complement-graph","display_name":"Complement graph","score":0.42324501276016235},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.27945196628570557},{"id":"https://openalex.org/keywords/1-planar-graph","display_name":"1-planar graph","score":0.18658611178398132}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7960339784622192},{"id":"https://openalex.org/C68996132","wikidata":"https://www.wikidata.org/wiki/Q3115485","display_name":"Foster graph","level":5,"score":0.693092942237854},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6842978000640869},{"id":"https://openalex.org/C197657726","wikidata":"https://www.wikidata.org/wiki/Q174733","display_name":"Bipartite graph","level":3,"score":0.6309505701065063},{"id":"https://openalex.org/C199692417","wikidata":"https://www.wikidata.org/wiki/Q7269362","display_name":"Quartic graph","level":5,"score":0.5741574168205261},{"id":"https://openalex.org/C100500283","wikidata":"https://www.wikidata.org/wiki/Q1374495","display_name":"Cubic graph","level":5,"score":0.5736172795295715},{"id":"https://openalex.org/C134119311","wikidata":"https://www.wikidata.org/wiki/Q913598","display_name":"Complete bipartite graph","level":4,"score":0.5096001625061035},{"id":"https://openalex.org/C200597783","wikidata":"https://www.wikidata.org/wiki/Q4391289","display_name":"Edge-transitive graph","level":5,"score":0.5067928433418274},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4959810674190521},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.4906529486179352},{"id":"https://openalex.org/C36038622","wikidata":"https://www.wikidata.org/wiki/Q5428703","display_name":"Factor-critical graph","level":5,"score":0.4850398898124695},{"id":"https://openalex.org/C166911692","wikidata":"https://www.wikidata.org/wiki/Q7130424","display_name":"Pancyclic graph","level":5,"score":0.46940314769744873},{"id":"https://openalex.org/C22149727","wikidata":"https://www.wikidata.org/wiki/Q7940747","display_name":"Voltage graph","level":4,"score":0.4351625442504883},{"id":"https://openalex.org/C168291704","wikidata":"https://www.wikidata.org/wiki/Q902252","display_name":"Complement graph","level":5,"score":0.42324501276016235},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.27945196628570557},{"id":"https://openalex.org/C102192266","wikidata":"https://www.wikidata.org/wiki/Q4545823","display_name":"1-planar graph","level":4,"score":0.18658611178398132}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.37236/10988","is_oa":true,"landing_page_url":"https://doi.org/10.37236/10988","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v30i2p5/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"},{"id":"pmh:oai:arXiv.org:2109.03060","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2109.03060","pdf_url":"https://arxiv.org/pdf/2109.03060","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:www.um.edu.mt:123456789/118843","is_oa":true,"landing_page_url":"https://www.um.edu.mt/library/oar/handle/123456789/118843","pdf_url":"https://www.um.edu.mt/library/oar/bitstream/123456789/118843/1/Betwixt_and_between_2_factor_Hamiltonian_and_perfect_matching_Hamiltonian_graphs_2023.pdf","source":{"id":"https://openalex.org/S4306400782","display_name":"OAR@UM (University of Malta)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I197854408","host_organization_name":"University of Malta","host_organization_lineage":["https://openalex.org/I197854408"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"},{"id":"mag:3198523402","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/2109.03060","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.2109.03060","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2109.03060","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"doi:10.37236/10988","is_oa":true,"landing_page_url":"https://doi.org/10.37236/10988","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v30i2p5/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":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3198523402.pdf"},"referenced_works_count":14,"referenced_works":["https://openalex.org/W1501182880","https://openalex.org/W1979879564","https://openalex.org/W1998621342","https://openalex.org/W2019627940","https://openalex.org/W2062084754","https://openalex.org/W2064142604","https://openalex.org/W2088131503","https://openalex.org/W2239845434","https://openalex.org/W2611093227","https://openalex.org/W3098202922","https://openalex.org/W3119766805","https://openalex.org/W3140032042","https://openalex.org/W3166347205","https://openalex.org/W3193161769"],"related_works":["https://openalex.org/W3193161769","https://openalex.org/W1560173187","https://openalex.org/W3120794560","https://openalex.org/W2740629715","https://openalex.org/W3141567130","https://openalex.org/W1555810828","https://openalex.org/W2096257156","https://openalex.org/W3098097398","https://openalex.org/W2047104722","https://openalex.org/W2121496532","https://openalex.org/W2093840085","https://openalex.org/W3104688290","https://openalex.org/W2950467368","https://openalex.org/W2952907380","https://openalex.org/W1982503413","https://openalex.org/W1845827952","https://openalex.org/W2979697317","https://openalex.org/W1778521510","https://openalex.org/W2091160220","https://openalex.org/W1999463304"],"abstract_inverted_index":{"A":[0,16],"Hamiltonian":[1,5,14,51,249],"graph":[2,27,72,136,140,160,176,181,192,230,266],"is":[3,12,21,32,65,151,161,196,215],"2-factor":[4],"(2FH)":[6],"if":[7,38,158,198,201],"each":[8,39],"of":[9,41,118,130,203],"its":[10,42,204],"2-factors":[11],"a":[13,26,29,50,70,74,131,135,159,162,190,240,248,265,268],"cycle.":[15,52],"similar,":[17],"but":[18,144],"weaker,":[19],"property":[20,24,37],"the":[22,57,87,113,116,128,139,142,173,179,212,222,237],"Perfect-Matching-Hamiltonian":[23],"(PMH-property):":[25],"admitting":[28,73,112,267],"perfect":[30,43,241],"matching":[31,242],"said":[33,83],"to":[34,49,76,101,217,247,270],"have":[35],"this":[36,91],"one":[40,96,253],"matchings":[44],"(1-factors)":[45],"can":[46,97,168,244],"be":[47,77,82,170,245],"extended":[48,246],"It":[53,153],"was":[54,154],"shown":[55],"that":[56,127,138,149,157,189,211],"star":[58,99,184],"product":[59],"operation":[60],"between":[61],"two":[62,259],"bipartite":[63,71,163,175,226],"2FH-graphs":[64],"necessary":[66,260],"and":[67,89,110,178,199,261,274],"sufficient":[68,262],"for":[69,264],"3-edge-cut":[75],"2FH.":[78,152],"The":[79],"same":[80],"cannot":[81],"when":[84],"dealing":[85],"with":[86,115,231],"PMH-property,":[88,143],"in":[90,134,251],"work":[92],"we":[93,122,187,256],"discuss":[94],"how":[95],"use":[98],"products":[100],"obtain":[102],"graphs":[103],"(which":[104],"are":[105,206],"not":[106,146],"necessarily":[107,147,194],"bipartite,":[108],"regular":[109],"2FH)":[111],"PMH-property":[114,238],"help":[117],"malleable":[119,132],"vertices,":[120],"which":[121,243],"introduce":[123],"here.":[124],"We":[125,208],"show":[126,188],"presence":[129],"vertex":[133],"implies":[137],"has":[141],"does":[145],"imply":[148],"it":[150,167],"also":[155,209,257],"conjectured":[156],"cubic":[164,191,229],"2FH-graph,":[165],"then":[166],"only":[169,200],"obtained":[171],"from":[172,221],"complete":[174],"$K_{3,3}$":[177],"Heawood":[180,223],"by":[182],"using":[183],"products.":[185],"Here,":[186],"(not":[193],"bipartite)":[195],"2FH":[197],"all":[202],"vertices":[205],"malleable.":[207],"prove":[210],"above":[213],"conjecture":[214],"equivalent":[216],"saying":[218],"that,":[219],"apart":[220],"graph,":[224],"every":[225],"cyclically":[227],"4-edge-connected":[228],"girth":[232],"at":[233],"least":[234],"6":[235],"having":[236],"admits":[239],"cycle":[250],"exactly":[252],"way.":[254],"Finally,":[255],"give":[258],"conditions":[263],"2-edge-cut":[269],"be:":[271],"(i)":[272],"2FH,":[273],"(ii)":[275],"PMH.":[276]},"counts_by_year":[],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}