{"id":"https://openalex.org/W7225227909","doi":"https://doi.org/10.5281/zenodo.23966079","title":"Counterexamples to the conjectured characterization of Hamiltonian degree sequences in digraphs","display_name":"Counterexamples to the conjectured characterization of Hamiltonian degree sequences in digraphs","publication_year":2026,"publication_date":"2026-11-04","ids":{"openalex":"https://openalex.org/W7225227909","doi":"https://doi.org/10.5281/zenodo.23966079"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.23966079","doi":"https://doi.org/10.5281/zenodo.23966079","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23966079","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"volume":null,"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.5281/zenodo.23966079","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5159121649","display_name":"P. Graham","orcid":"https://orcid.org/0009-0007-8493-1505","observed_orcids":["https://orcid.org/0009-0007-8493-1505"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Graham, P.","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0009-0007-8493-1505","affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5159121649"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9984999895095825,"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":0.9984999895095825,"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":0.0008999999845400453,"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/T11166","display_name":"Analytic Number Theory Research","score":0.0,"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"}}],"keywords":[],"concepts":[{"id":"https://openalex.org/C162838799","wikidata":"https://www.wikidata.org/wiki/Q596077","display_name":"Counterexample","level":2,"score":0.960099995136261},{"id":"https://openalex.org/C2779145032","wikidata":"https://www.wikidata.org/wiki/Q191494","display_name":"Digraph","level":2,"score":0.8862000107765198},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.8720999956130981},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.78329998254776},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6552000045776367},{"id":"https://openalex.org/C2780841128","wikidata":"https://www.wikidata.org/wiki/Q5073781","display_name":"Characterization (materials science)","level":2,"score":0.5214999914169312},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.4690000116825104},{"id":"https://openalex.org/C130787639","wikidata":"https://www.wikidata.org/wiki/Q5645293","display_name":"Hamiltonian (control theory)","level":2,"score":0.45739999413490295},{"id":"https://openalex.org/C197115733","wikidata":"https://www.wikidata.org/wiki/Q1003136","display_name":"Forcing (mathematics)","level":2,"score":0.454800009727478},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.4489000141620636},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.43959999084472656},{"id":"https://openalex.org/C78635031","wikidata":"https://www.wikidata.org/wiki/Q6671695","display_name":"Lonely runner conjecture","level":4,"score":0.3644999861717224},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.36079999804496765},{"id":"https://openalex.org/C117354338","wikidata":"https://www.wikidata.org/wiki/Q1165112","display_name":"Singleton","level":3,"score":0.33090001344680786},{"id":"https://openalex.org/C86524685","wikidata":"https://www.wikidata.org/wiki/Q273037","display_name":"Hamiltonian path","level":3,"score":0.326200008392334},{"id":"https://openalex.org/C38754835","wikidata":"https://www.wikidata.org/wiki/Q2003238","display_name":"Strongly connected component","level":2,"score":0.2840000092983246},{"id":"https://openalex.org/C128814272","wikidata":"https://www.wikidata.org/wiki/Q837314","display_name":"Collatz conjecture","level":3,"score":0.2705000042915344}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.5281/zenodo.23966079","doi":"https://doi.org/10.5281/zenodo.23966079","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23966079","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},{"id":"doi:10.5281/zenodo.23966080","doi":"https://doi.org/10.5281/zenodo.23966080","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23966080","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.5281/zenodo.23966079","doi":"https://doi.org/10.5281/zenodo.23966079","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23966079","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W1966985679","https://openalex.org/W2000934872","https://openalex.org/W2018724658","https://openalex.org/W2036286064","https://openalex.org/W2081397477","https://openalex.org/W2121104987","https://openalex.org/W2157737769","https://openalex.org/W2981188613","https://openalex.org/W3178506813","https://openalex.org/W4408649186","https://openalex.org/W7220936861"],"related_works":[],"abstract_inverted_index":{"We":[0],"show":[1],"that":[2,36,152,162],"the":[3,14,55,75,91,102,111,126,148,166,211,215,228,242],"conjecture":[4,66,84,136,170],"of":[5,67,74,108,168,180],"K\u00fchn,":[6],"Osthus":[7,189],"and":[8,29,43,50,89,99,101,121,125,147,188,192,214,224],"Treglown":[9],"(2008),":[10],"which":[11,69],"would":[12],"characterize":[13],"degree":[15],"sequences":[16,45],"forcing":[17],"a":[18,22,51,60,175,183],"Hamilton":[19,61],"cycle":[20,176],"in":[21,87,141,198],"digraph,":[23],"fails":[24,137],"for":[25,31,138,155,163],"every":[26,37,139,164,178],"order":[27,56],"$n\\ge7$":[28],"holds":[30,154],"$3\\le":[32,156],"n\\le6$.":[33],"It":[34,63],"states":[35],"digraph":[38,120],"whose":[39],"separately":[40],"sorted":[41],"out-":[42],"in-degree":[44],"satisfy":[46],"two":[47],"Chv\u00e1tal-type":[48],"conditions,":[49],"third":[52,76,112],"condition":[53],"when":[54],"is":[57],"even,":[58],"has":[59,202],"cycle.":[62],"strengthens":[64],"Nash-Williams'":[65,83,135],"1975,":[68],"assumes":[70],"strong":[71],"connectivity":[72],"instead":[73],"condition.":[77,113],"Guninski":[78],"found":[79],"6-vertex":[80],"counterexamples":[81,115,195],"to":[82,143],"on":[85],"MathOverflow":[86],"2013":[88,92],"2020;":[90],"example":[93],"was":[94],"confirmed":[95],"there":[96],"by":[97,105,131,186,207,219,235,238],"Royle":[98],"Thomas":[100],"2020":[103],"ones":[104],"DeBiasio.":[106],"All":[107],"them":[109],"violate":[110],"Our":[114],"are":[116,129,196],"an":[117,122],"explicit":[118,123],"7-vertex":[119],"family,":[124],"small":[127],"orders":[128],"settled":[130],"exhaustive":[132],"search.":[133],"Hence":[134],"$n\\ge7$,":[140],"addition":[142],"Guninski's":[144],"case":[145],"$n=6$,":[146],"same":[149],"search":[150],"shows":[151,161],"it":[153],"n\\le5$.":[157],"The":[158,194,209],"family":[159],"also":[160],"$n\\ge8$":[165],"conditions":[167],"either":[169],"do":[171],"not":[172,203,232],"even":[173],"force":[174],"through":[177],"pair":[179],"vertices,":[181],"answering":[182],"question":[184],"recorded":[185],"K\u00fchn":[187],"after":[190],"Bermond":[191],"Thomassen.":[193],"checked":[197],"Lean.":[199],"This":[200],"work":[201],"yet":[204,233],"been":[205],"reviewed":[206,234],"experts.":[208,236],"proofs,":[210],"Lean":[212],"formalization":[213],"text":[216],"were":[217],"produced":[218],"AI":[220,239],"models":[221,240],"(from":[222],"OpenAI":[223],"Anthropic),":[225],"working":[226],"under":[227,241],"author's":[229,243],"direction.":[230,244],"Computer-assisted;":[231],"Produced":[237]},"counts_by_year":[],"updated_date":"2026-11-05T12:25:35.769452","created_date":"2026-11-05T00:00:00"}