{"id":"https://openalex.org/W2770316888","doi":"https://doi.org/10.37236/7187","title":"The $r$-Matching Sequencibility of Complete Graphs","display_name":"The $r$-Matching Sequencibility of Complete Graphs","publication_year":2018,"publication_date":"2018-01-12","ids":{"openalex":"https://openalex.org/W2770316888","doi":"https://doi.org/10.37236/7187","mag":"2770316888"},"language":"en","primary_location":{"id":"doi:10.37236/7187","is_oa":true,"landing_page_url":"https://doi.org/10.37236/7187","pdf_url":null,"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://doi.org/10.37236/7187","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5002486020","display_name":"Adam Mammoliti","orcid":"https://orcid.org/0000-0003-1476-1225"},"institutions":[{"id":"https://openalex.org/I31746571","display_name":"UNSW Sydney","ror":"https://ror.org/03r8z3t63","country_code":"AU","type":"education","lineage":["https://openalex.org/I31746571"]}],"countries":["AU"],"is_corresponding":true,"raw_author_name":"Adam Mammoliti","raw_affiliation_strings":["UNSW Sydney","UNSW SYDNEY"],"affiliations":[{"raw_affiliation_string":"UNSW Sydney","institution_ids":["https://openalex.org/I31746571"]},{"raw_affiliation_string":"UNSW SYDNEY","institution_ids":["https://openalex.org/I31746571"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5002486020"],"corresponding_institution_ids":["https://openalex.org/I31746571"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.10075733,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"25","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/T10374","display_name":"Advanced Graph Theory Research","score":0.9993000030517578,"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":0.9958999752998352,"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":0.9077498912811279},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8160285949707031},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.6361211538314819},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.600342333316803},{"id":"https://openalex.org/keywords/hypergraph","display_name":"Hypergraph","score":0.5524533987045288},{"id":"https://openalex.org/keywords/matching","display_name":"Matching (statistics)","score":0.5089142322540283},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.49399930238723755},{"id":"https://openalex.org/keywords/complete-graph","display_name":"Complete graph","score":0.43668726086616516}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.9077498912811279},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8160285949707031},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.6361211538314819},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.600342333316803},{"id":"https://openalex.org/C2781221856","wikidata":"https://www.wikidata.org/wiki/Q840247","display_name":"Hypergraph","level":2,"score":0.5524533987045288},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.5089142322540283},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.49399930238723755},{"id":"https://openalex.org/C125080357","wikidata":"https://www.wikidata.org/wiki/Q45715","display_name":"Complete graph","level":3,"score":0.43668726086616516},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.37236/7187","is_oa":true,"landing_page_url":"https://doi.org/10.37236/7187","pdf_url":null,"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:1711.05013","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1711.05013","pdf_url":"https://arxiv.org/pdf/1711.05013","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":"","raw_type":"text"},{"id":"mag:2770316888","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1711.05013.pdf","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.1711.05013","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1711.05013","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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"doi:10.37236/7187","is_oa":true,"landing_page_url":"https://doi.org/10.37236/7187","pdf_url":null,"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":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":2,"referenced_works":["https://openalex.org/W2001684394","https://openalex.org/W2029330971"],"related_works":["https://openalex.org/W2810391841","https://openalex.org/W3098406359","https://openalex.org/W2963617211","https://openalex.org/W2224867982","https://openalex.org/W2518307406","https://openalex.org/W2510210601","https://openalex.org/W2952059987","https://openalex.org/W2943841550","https://openalex.org/W3086553150","https://openalex.org/W3205324233","https://openalex.org/W3128450046","https://openalex.org/W2181694489","https://openalex.org/W2967496539","https://openalex.org/W2962811018","https://openalex.org/W2951109691","https://openalex.org/W2071732668","https://openalex.org/W3201939494","https://openalex.org/W2002645285","https://openalex.org/W3200271267","https://openalex.org/W1993446652"],"abstract_inverted_index":{"Alspach":[0,47],"[":[1],"Bull.":[2],"Inst.":[3],"Combin.":[4],"Appl.,":[5],"52":[6],"(2008),":[7],"pp.":[8,62],"7--20]":[9],"defined":[10],"the":[11,23,34,65,115,128,162],"maximal":[12],"matching":[13,69],"sequencibility":[14,70],"of":[15,33,36,71,164,172,189],"a":[16,45,72,101,120],"graph":[17,73,121],"$G$,":[18,74],"denoted":[19,75],"$ms(G)$,":[20],"to":[21,67,93],"be":[22],"largest":[24],"integer":[25],"$s$":[26,41,97],"for":[27,119,127,151,161],"which":[28,77],"there":[29],"is":[30],"an":[31],"ordering":[32],"edges":[35,43,99],"$G$":[37,122],"such":[38,117],"that":[39,50,83,95,136,146],"every":[40,96,104],"consecutive":[42,98],"form":[44,100],"matching.":[46],"also":[48,175],"proved":[49,82],"$ms(K_n)":[51],"=":[52,85,138],"\\bigl\\lfloor\\frac{n-1}{2}\\bigr\\rfloor$.":[53],"Brualdi":[54],"et":[55],"al.":[56],"[Australas.":[57],"J.":[58],"Combin.,":[59],"53":[60],"(2012),":[61],"245--256]":[63],"extended":[64],"definition":[66],"cyclic":[68,131],"$cms(G)$,":[76],"allows":[78],"cyclical":[79],"orderings":[80],"and":[81,112,125,130,140,145,154,168,180,191],"$cms(K_n)":[84],"\\bigl\\lfloor\\frac{n-2}{2}\\bigr\\rfloor$.In":[86],"this":[87],"paper,":[88],"we":[89,113],"generalise":[90],"these":[91,158],"definitions":[92],"require":[94],"subgraph":[102],"where":[103],"vertex":[105],"has":[106],"degree":[107],"at":[108],"most":[109],"$r\\geq":[110],"1$,":[111],"denote":[114],"maximum":[116],"number":[118],"by":[123,166],"$ms_r(G)$":[124,179,190],"$cms_r(G)$":[126,181],"non-cyclic":[129],"cases,":[132,165],"respectively.":[133],"We":[134,156,174],"conjecture":[135],"$ms_r(K_n)":[137],"\\bigl\\lfloor\\frac{rn-1}{2}\\bigr\\rfloor$":[139,144],"${\\bigl\\lfloor\\frac{rn-1}{2}\\bigr\\rfloor-1}\\leq":[141],"cms_r(K_n)":[142],"\\leq":[143],"both":[147],"bounds":[148,177],"are":[149],"attained":[150],"some":[152],"$r$":[153],"$n$.":[155],"prove":[157],"conjectured":[159],"identities":[160],"majority":[163],"defining":[167],"characterising":[169],"selected":[170],"decompositions":[171],"$K_n$.":[173],"provide":[176],"on":[178,186],"as":[182,184],"well":[183],"results":[185],"hypergraph":[187],"analogues":[188],"$cms_r(G)$.":[192]},"counts_by_year":[],"updated_date":"2026-02-09T09:26:11.010843","created_date":"2025-10-10T00:00:00"}
