{"id":"https://openalex.org/W4416445196","doi":"https://doi.org/10.4230/lipics.socg.2026.22","title":"Disproving Two Conjectures on the Hamiltonicity of Venn Diagrams","display_name":"Disproving Two Conjectures on the Hamiltonicity of Venn Diagrams","publication_year":2025,"publication_date":"2025-03-24","ids":{"openalex":"https://openalex.org/W4416445196","doi":"https://doi.org/10.4230/lipics.socg.2026.22"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2503.18554","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2503.18554","pdf_url":"https://arxiv.org/pdf/2503.18554","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"},"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2503.18554","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5022706828","display_name":"Sofia Brenner","orcid":"https://orcid.org/0009-0006-8512-2569"},"institutions":[{"id":"https://openalex.org/I106157433","display_name":"University of Kassel","ror":"https://ror.org/04zc7p361","country_code":"DE","type":"education","lineage":["https://openalex.org/I106157433"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Brenner, Sofia","raw_affiliation_strings":["Institute of Mathematics, University of Kassel, Germany"],"raw_orcid":"https://orcid.org/0009-0006-8512-2569","affiliations":[{"raw_affiliation_string":"Institute of Mathematics, University of Kassel, Germany","institution_ids":["https://openalex.org/I106157433"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5090048794","display_name":"Linda Kleist","orcid":"https://orcid.org/0000-0002-3786-916X"},"institutions":[{"id":"https://openalex.org/I159176309","display_name":"Universit\u00e4t Hamburg","ror":"https://ror.org/00g30e956","country_code":"DE","type":"education","lineage":["https://openalex.org/I159176309"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Kleist, Linda","raw_affiliation_strings":["Department of Informatics, University of Hamburg, Germany"],"raw_orcid":"https://orcid.org/0000-0002-3786-916X","affiliations":[{"raw_affiliation_string":"Department of Informatics, University of Hamburg, Germany","institution_ids":["https://openalex.org/I159176309"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5028248747","display_name":"Torsten M\u00fctze","orcid":"https://orcid.org/0000-0002-6383-7436"},"institutions":[{"id":"https://openalex.org/I106157433","display_name":"University of Kassel","ror":"https://ror.org/04zc7p361","country_code":"DE","type":"education","lineage":["https://openalex.org/I106157433"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"M\u00fctze, Torsten","raw_affiliation_strings":["Institute of Mathematics, University of Kassel, Germany"],"raw_orcid":"https://orcid.org/0000-0002-6383-7436","affiliations":[{"raw_affiliation_string":"Institute of Mathematics, University of Kassel, Germany","institution_ids":["https://openalex.org/I106157433"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5069173698","display_name":"Christian Rieck","orcid":"https://orcid.org/0000-0003-0846-5163"},"institutions":[{"id":"https://openalex.org/I106157433","display_name":"University of Kassel","ror":"https://ror.org/04zc7p361","country_code":"DE","type":"education","lineage":["https://openalex.org/I106157433"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Rieck, Christian","raw_affiliation_strings":["Institute of Mathematics, University of Kassel, Germany"],"raw_orcid":"https://orcid.org/0000-0003-0846-5163","affiliations":[{"raw_affiliation_string":"Institute of Mathematics, University of Kassel, Germany","institution_ids":["https://openalex.org/I106157433"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5093227465","display_name":"Francesco Verciani","orcid":null},"institutions":[{"id":"https://openalex.org/I106157433","display_name":"University of Kassel","ror":"https://ror.org/04zc7p361","country_code":"DE","type":"education","lineage":["https://openalex.org/I106157433"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Verciani, Francesco","raw_affiliation_strings":["Institute of Mathematics, University of Kassel, Germany"],"raw_orcid":"https://orcid.org/0009-0000-0536-8646","affiliations":[{"raw_affiliation_string":"Institute of Mathematics, University of Kassel, Germany","institution_ids":["https://openalex.org/I106157433"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9120000004768372,"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9120000004768372,"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/T12069","display_name":"Commutative Algebra and Its Applications","score":0.039799999445676804,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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/T11435","display_name":"Polynomial and algebraic computation","score":0.011300000362098217,"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/venn-diagram","display_name":"Venn diagram","score":0.9857000112533569},{"id":"https://openalex.org/keywords/counterexample","display_name":"Counterexample","score":0.7529000043869019},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.6680999994277954},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.5475000143051147},{"id":"https://openalex.org/keywords/axiom-of-choice","display_name":"Axiom of choice","score":0.3986000120639801},{"id":"https://openalex.org/keywords/statement","display_name":"Statement (logic)","score":0.36039999127388}],"concepts":[{"id":"https://openalex.org/C55508974","wikidata":"https://www.wikidata.org/wiki/Q190763","display_name":"Venn diagram","level":2,"score":0.9857000112533569},{"id":"https://openalex.org/C162838799","wikidata":"https://www.wikidata.org/wiki/Q596077","display_name":"Counterexample","level":2,"score":0.7529000043869019},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7315999865531921},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.6680999994277954},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.5475000143051147},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5378999710083008},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4885999858379364},{"id":"https://openalex.org/C151797676","wikidata":"https://www.wikidata.org/wiki/Q179692","display_name":"Axiom of choice","level":4,"score":0.3986000120639801},{"id":"https://openalex.org/C2777026412","wikidata":"https://www.wikidata.org/wiki/Q2684591","display_name":"Statement (logic)","level":2,"score":0.36039999127388},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.3578000068664551},{"id":"https://openalex.org/C186399060","wikidata":"https://www.wikidata.org/wiki/Q959962","display_name":"Diagram","level":2,"score":0.31949999928474426},{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.3059999942779541},{"id":"https://openalex.org/C2780801425","wikidata":"https://www.wikidata.org/wiki/Q5164392","display_name":"Construct (python library)","level":2,"score":0.2759999930858612},{"id":"https://openalex.org/C168054591","wikidata":"https://www.wikidata.org/wiki/Q17152869","display_name":"Story-driven modeling","level":5,"score":0.2678000032901764}],"mesh":[],"locations_count":5,"locations":[{"id":"pmh:oai:arXiv.org:2503.18554","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2503.18554","pdf_url":"https://arxiv.org/pdf/2503.18554","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:drops-oai.dagstuhl.de:25828","is_oa":true,"landing_page_url":"https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2026.22","pdf_url":"https://drops.dagstuhl.de/storage/00lipics/lipics-vol367-socg2026/LIPIcs.SoCG.2026.22/LIPIcs.SoCG.2026.22.pdf","source":{"id":"https://openalex.org/S4377196569","display_name":"DROPS (Schloss Dagstuhl \u2013 Leibniz Center for Informatics)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2799853480","host_organization_name":"Schloss Dagstuhl \u2013 Leibniz Center for Informatics","host_organization_lineage":["https://openalex.org/I2799853480"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"InProceedings"},{"id":"pmh:doi:10.4230/lipics.socg.2026.22","is_oa":true,"landing_page_url":"https://tmuetze.de/papers/venn.zip","pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"ConferencePaper"},{"id":"doi:10.48550/arxiv.2503.18554","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2503.18554","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":"Preprint"},{"id":"doi:10.4230/lipics.socg.2026.22","is_oa":true,"landing_page_url":"https://doi.org/10.4230/lipics.socg.2026.22","pdf_url":null,"source":{"id":"https://openalex.org/S7407052059","display_name":"Dagstuhl Research Online Publication Server","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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":"ConferencePaper"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2503.18554","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2503.18554","pdf_url":"https://arxiv.org/pdf/2503.18554","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"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"In":[0,43],"1984,":[1],"Winkler":[2],"conjectured":[3,129],"that":[4,30,113,130],"every":[5,121],"simple":[6,17,36,66,122],"Venn":[7,18,37,67,101,123],"diagram":[8,19,38,124],"with":[9,20,69,125],"n":[10,54,70,126,145],"curves":[11,73],"can":[12],"be":[13],"extended":[14],"to":[15,27,49,140],"a":[16,40,100,117],"n+1":[21],"curves.":[22],"This":[23],"conjecture":[24,51,91,142],"is":[25],"equivalent":[26],"the":[28,31,93,96],"statement":[29],"dual":[32],"graph":[33,98,115],"of":[34,59,95,99],"any":[35],"has":[39,116],"Hamilton":[41,118],"cycle.":[42],"this":[44,60,114,131,141],"work,":[45],"we":[46,62,83],"construct":[47,138],"counterexamples":[48,139],"Winkler\u2019s":[50,107],"for":[52,120,134,143],"all":[53,64,144],"\u2265":[55,146],"6.":[56],"As":[57],"part":[58],"proof,":[61],"computed":[63],"3.430.404":[65],"diagrams":[68],"=":[71],"6":[72],"(even":[74],"their":[75],"number":[76],"was":[77],"not":[78],"previously":[79],"known),":[80],"among":[81],"which":[82],"found":[84],"72":[85],"counterexamples.":[86],"We":[87,137],"also":[88,132],"disprove":[89],"another":[90],"about":[92],"Hamiltonicity":[94],"arrangement":[97],"diagram.":[102],"Specifically,":[103],"while":[104],"working":[105],"on":[106],"conjecture,":[108],"Pruesse":[109],"and":[110,128],"Ruskey":[111],"proved":[112],"cycle":[119],"curves,":[127],"holds":[133],"non-simple":[135],"diagrams.":[136],"4.":[147]},"counts_by_year":[],"updated_date":"2026-07-25T09:21:30.201066","created_date":"2025-10-10T00:00:00"}