{"id":"https://openalex.org/W2810681272","doi":"https://doi.org/10.37236/7969","title":"Decomposable Twofold Triple Systems with Non-Hamiltonian 2-Block Intersection Graphs","display_name":"Decomposable Twofold Triple Systems with Non-Hamiltonian 2-Block Intersection Graphs","publication_year":2020,"publication_date":"2020-12-24","ids":{"openalex":"https://openalex.org/W2810681272","doi":"https://doi.org/10.37236/7969","mag":"2810681272"},"language":"en","primary_location":{"id":"doi:10.37236/7969","is_oa":true,"landing_page_url":"https://doi.org/10.37236/7969","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v27i4p57/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":["crossref","datacite","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v27i4p57/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5077214421","display_name":"Rosalind A. Cameron","orcid":null},"institutions":[{"id":"https://openalex.org/I130438778","display_name":"Memorial University of Newfoundland","ror":"https://ror.org/04haebc03","country_code":"CA","type":"education","lineage":["https://openalex.org/I130438778"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"Rosalind A. Cameron","raw_affiliation_strings":["Memorial University of Newfoundland"],"affiliations":[{"raw_affiliation_string":"Memorial University of Newfoundland","institution_ids":["https://openalex.org/I130438778"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5087426538","display_name":"David A. Pike","orcid":"https://orcid.org/0000-0001-8952-3016"},"institutions":[{"id":"https://openalex.org/I130438778","display_name":"Memorial University of Newfoundland","ror":"https://ror.org/04haebc03","country_code":"CA","type":"education","lineage":["https://openalex.org/I130438778"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"David A. Pike","raw_affiliation_strings":["Memorial University of Newfoundland"],"affiliations":[{"raw_affiliation_string":"Memorial University of Newfoundland","institution_ids":["https://openalex.org/I130438778"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5077214421"],"corresponding_institution_ids":["https://openalex.org/I130438778"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.00181238,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"27","issue":"4","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":0.9998999834060669,"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":0.9998999834060669,"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":0.998199999332428,"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":0.9979000091552734,"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/bipartite-graph","display_name":"Bipartite graph","score":0.8407588005065918},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8354238867759705},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7321600317955017},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.6144098043441772},{"id":"https://openalex.org/keywords/hamiltonian-path","display_name":"Hamiltonian path","score":0.5628364682197571},{"id":"https://openalex.org/keywords/hamiltonian","display_name":"Hamiltonian (control theory)","score":0.5618762373924255},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.5380864143371582},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.45878058671951294},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4067540466785431}],"concepts":[{"id":"https://openalex.org/C197657726","wikidata":"https://www.wikidata.org/wiki/Q174733","display_name":"Bipartite graph","level":3,"score":0.8407588005065918},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8354238867759705},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7321600317955017},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.6144098043441772},{"id":"https://openalex.org/C86524685","wikidata":"https://www.wikidata.org/wiki/Q273037","display_name":"Hamiltonian path","level":3,"score":0.5628364682197571},{"id":"https://openalex.org/C130787639","wikidata":"https://www.wikidata.org/wiki/Q5645293","display_name":"Hamiltonian (control theory)","level":2,"score":0.5618762373924255},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.5380864143371582},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.45878058671951294},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4067540466785431},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.37236/7969","is_oa":true,"landing_page_url":"https://doi.org/10.37236/7969","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v27i4p57/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":"mag:2810681272","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1806.11080","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.1806.11080","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1806.11080","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:10.37236/7969","is_oa":true,"landing_page_url":"https://doi.org/10.37236/7969","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v27i4p57/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":[{"id":"https://openalex.org/G1597412403","display_name":null,"funder_award_id":"RGPIN-","funder_id":"https://openalex.org/F4320334593","funder_display_name":"Natural Sciences and Engineering Research Council of Canada"},{"id":"https://openalex.org/G2165548363","display_name":null,"funder_award_id":"Canada","funder_id":"https://openalex.org/F4320334593","funder_display_name":"Natural Sciences and Engineering Research Council of Canada"},{"id":"https://openalex.org/G3216283581","display_name":null,"funder_award_id":"RGPIN-201","funder_id":"https://openalex.org/F4320334593","funder_display_name":"Natural Sciences and Engineering Research Council of Canada"},{"id":"https://openalex.org/G6221715925","display_name":null,"funder_award_id":"RGPIN","funder_id":"https://openalex.org/F4320334593","funder_display_name":"Natural Sciences and Engineering Research Council of Canada"}],"funders":[{"id":"https://openalex.org/F4320314000","display_name":"Compute Canada","ror":"https://ror.org/03ty8yr27"},{"id":"https://openalex.org/F4320314005","display_name":"Western Canada Research Grid","ror":null},{"id":"https://openalex.org/F4320323319","display_name":"Memorial University of Newfoundland","ror":"https://ror.org/04haebc03"},{"id":"https://openalex.org/F4320334593","display_name":"Natural Sciences and Engineering Research Council of Canada","ror":"https://ror.org/01h531d29"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2810681272.pdf","grobid_xml":"https://content.openalex.org/works/W2810681272.grobid-xml"},"referenced_works_count":16,"referenced_works":["https://openalex.org/W120996398","https://openalex.org/W1484040084","https://openalex.org/W1910282425","https://openalex.org/W1995977838","https://openalex.org/W2015468112","https://openalex.org/W2037688303","https://openalex.org/W2060787934","https://openalex.org/W2087818742","https://openalex.org/W2313586032","https://openalex.org/W2909080107","https://openalex.org/W2949148515","https://openalex.org/W6601578400","https://openalex.org/W6603851090","https://openalex.org/W6611119050","https://openalex.org/W6807578206","https://openalex.org/W6825617235"],"related_works":["https://openalex.org/W3114520403","https://openalex.org/W2175639978","https://openalex.org/W1986731883","https://openalex.org/W33991549","https://openalex.org/W2026359334","https://openalex.org/W2508684685","https://openalex.org/W2135700202","https://openalex.org/W2624949604","https://openalex.org/W587872962","https://openalex.org/W3202151190","https://openalex.org/W2251473351","https://openalex.org/W2188781753","https://openalex.org/W2741424603","https://openalex.org/W1610997373","https://openalex.org/W1627709653","https://openalex.org/W2255281874","https://openalex.org/W2102488782","https://openalex.org/W2142636032","https://openalex.org/W1905847221","https://openalex.org/W2950123464"],"abstract_inverted_index":{"The":[0,42],"$2$-block":[1],"intersection":[2],"graph":[3,13],"($2$-BIG)":[4],"of":[5,19,22,162],"a":[6,55,79,83,115,134,147,153,157],"twofold":[7],"triple":[8,68],"system":[9],"(TTS)":[10],"is":[11,17,50,57,63,78,94,119,131,138,166],"the":[12,20,23,34,61,160,163],"whose":[14,117,136],"vertex":[15],"set":[16],"composed":[18],"blocks":[21,36],"TTS":[24,62],"and":[25,52,54,121,141,143,169],"two":[26,40,66],"vertices":[27],"are":[28,44],"joined":[29],"by":[30,87],"an":[31,98],"edge":[32],"if":[33,107],"corresponding":[35],"intersect":[37],"in":[38,89,151],"exactly":[39,59],"elements.":[41],"$2$-BIGs":[43],"themselves":[45],"interesting":[46],"graphs:":[47],"each":[48],"component":[49],"cubic":[51],"$3$-connected,":[53],"$2$-BIG":[56,73,118,137,161],"bipartite":[58,72,120,140,167],"when":[60],"decomposable":[64],"to":[65,82,132],"Steiner":[67],"systems.":[69],"Any":[70],"connected":[71,122,139,168],"with":[74],"no":[75],"Hamilton":[76],"cycle":[77],"further":[80],"counter-example":[81],"disproved":[84],"conjecture":[85],"posed":[86],"Tutte":[88],"1971.":[90],"Our":[91,129],"main":[92],"result":[93],"that":[95,102],"there":[96,113],"exists":[97,114],"integer":[99],"$N$":[100],"such":[101,152],"for":[103],"all":[104],"$v\\geq":[105],"N$,":[106],"$v\\equiv":[108],"1$":[109],"or":[110],"$3\\mod{6}$":[111],"then":[112],"TTS($v$)":[116,148,165],"but":[123],"not":[124],"Hamiltonian.":[125],"Furthermore,":[126],"$13<N\\leq":[127],"663$.":[128],"approach":[130],"construct":[133],"TTS($u$)":[135],"non-Hamiltonian":[142],"embed":[144],"it":[145],"within":[146],"where":[149],"$v>2u$":[150],"way":[154],"that,":[155],"after":[156],"single":[158],"trade,":[159],"resulting":[164],"non-Hamiltonian.":[170]},"counts_by_year":[],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}