{"id":"https://openalex.org/W7207747730","doi":"https://doi.org/10.48550/arxiv.2609.02249","title":"Hamiltonicity of graphs of acyclic orientations and acyclic polynomials","display_name":"Hamiltonicity of graphs of acyclic orientations and acyclic polynomials","publication_year":2026,"publication_date":"2026-09-02","ids":{"openalex":"https://openalex.org/W7207747730","doi":"https://doi.org/10.48550/arxiv.2609.02249"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.02249","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.02249","pdf_url":"https://arxiv.org/pdf/2609.02249","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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"},"volume":null,"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.02249","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5092467498","display_name":"Leonie M\u00fchlherr","orcid":"https://orcid.org/0009-0000-9900-7242","observed_orcids":["https://orcid.org/0009-0000-9900-7242"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"M\u00fchlherr, Leonie","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5037347520","display_name":"Germain Poullot","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Poullot, Germain","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"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":0.6259999871253967,"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":0.6259999871253967,"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":0.3621000051498413,"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/T11476","display_name":"Graph theory and applications","score":0.004600000102072954,"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/acyclic-orientations","display_name":"acyclic orientations","score":0.9520000219345093},{"id":"https://openalex.org/keywords/hamiltonicity","display_name":"Hamiltonicity","score":0.6639999747276306},{"id":"https://openalex.org/keywords/multipath-propagation","display_name":"multipath propagation","score":0.8640000224113464},{"id":"https://openalex.org/keywords/ear-decomposition","display_name":"ear decomposition","score":0.8460000157356262},{"id":"https://openalex.org/keywords/biconnected-graphs","display_name":"2-connected graphs","score":0.8560000061988831},{"id":"https://openalex.org/keywords/parity-problem","display_name":"parity problem","score":0.7110000252723694},{"id":"https://openalex.org/keywords/deletion-contraction","display_name":"deletion-contraction","score":0.9470000267028809}],"concepts":[{"id":"https://openalex.org/C74197172","wikidata":"https://www.wikidata.org/wiki/Q1195339","display_name":"Directed acyclic graph","level":2,"score":0.8723000288009644},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6241000294685364},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5767999887466431},{"id":"https://openalex.org/C146380142","wikidata":"https://www.wikidata.org/wiki/Q1137726","display_name":"Directed graph","level":2,"score":0.5351999998092651},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5314000248908997},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.45320001244544983},{"id":"https://openalex.org/C198414033","wikidata":"https://www.wikidata.org/wiki/Q5155607","display_name":"Comparability graph","level":5,"score":0.4065000116825104},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.39739999175071716},{"id":"https://openalex.org/C125792925","wikidata":"https://www.wikidata.org/wiki/Q3115604","display_name":"Outerplanar graph","level":5,"score":0.3278999924659729},{"id":"https://openalex.org/C2778753846","wikidata":"https://www.wikidata.org/wiki/Q6554239","display_name":"Link (geometry)","level":2,"score":0.30970001220703125},{"id":"https://openalex.org/C5737132","wikidata":"https://www.wikidata.org/wiki/Q1101814","display_name":"Clique-width","level":5,"score":0.30250000953674316},{"id":"https://openalex.org/C180222743","wikidata":"https://www.wikidata.org/wiki/Q4942980","display_name":"Book embedding","level":5,"score":0.2971999943256378},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2856999933719635},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.2802000045776367},{"id":"https://openalex.org/C86524685","wikidata":"https://www.wikidata.org/wiki/Q273037","display_name":"Hamiltonian path","level":3,"score":0.2718999981880188},{"id":"https://openalex.org/C88230418","wikidata":"https://www.wikidata.org/wiki/Q131476","display_name":"Graph theory","level":2,"score":0.2671999931335449},{"id":"https://openalex.org/C192209626","wikidata":"https://www.wikidata.org/wiki/Q190909","display_name":"Focus (optics)","level":2,"score":0.2651999890804291},{"id":"https://openalex.org/C64339825","wikidata":"https://www.wikidata.org/wiki/Q722659","display_name":"Graph property","level":5,"score":0.26260000467300415},{"id":"https://openalex.org/C53052385","wikidata":"https://www.wikidata.org/wiki/Q17104046","display_name":"Mixed graph","level":5,"score":0.25920000672340393},{"id":"https://openalex.org/C22149727","wikidata":"https://www.wikidata.org/wiki/Q7940747","display_name":"Voltage graph","level":4,"score":0.25220000743865967}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.02249","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.02249","pdf_url":"https://arxiv.org/pdf/2609.02249","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"doi:10.48550/arxiv.2609.02249","doi":"https://doi.org/10.48550/arxiv.2609.02249","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.02249","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.02249","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.02249","pdf_url":"https://arxiv.org/pdf/2609.02249","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7207747730.pdf","grobid_xml":"https://content.openalex.org/works/W7207747730.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W1746068744","https://openalex.org/W7098203661","https://openalex.org/W156470527","https://openalex.org/W1985403606","https://openalex.org/W7009607107","https://openalex.org/W1999645947","https://openalex.org/W4316652454","https://openalex.org/W1980593972","https://openalex.org/W4235361374","https://openalex.org/W7135179352"],"abstract_inverted_index":{"We":[0,155],"study":[1],"the":[2,24,35,38,49,71,91,114,120,129,145,160,170],"graph":[3,10,19,79,127],"$\\mathcal{AO}(G)$":[4],"of":[5,8,26,37,44,52,73,88,95,102,122,125,144,148,159,169],"acyclic":[6,13,115,123,146,161],"orientations":[7,14,124],"a":[9,27,68,74,77,107,126,142,179],"$G$.":[11],"Two":[12],"are":[15,63,166],"adjacent":[16],"in":[17],"this":[18],"if":[20,138],"they":[21,165,176],"disagree":[22],"on":[23,34,76],"orientation":[25],"single":[28],"arc.":[29],"In":[30,110],"particular,":[31],"we":[32,59,66,98,112],"focus":[33],"Hamiltonicity":[36],"graphs":[39],"$\\mathcal{AO}(G)$.":[40],"Using":[41],"two":[42],"methods":[43],"pattern":[45],"lacing":[46],"which":[47,61],"generalize":[48],"zig-zag":[50],"method":[51],"Brenner,":[53],"Cardinal,":[54],"McConville,":[55],"Merino":[56],"and":[57,128,136],"M\u00fctze,":[58],"characterize":[60],"multipaths":[62,105],"$\\mathcal{AO}$-Hamiltonian.":[64,154],"Moreover,":[65],"give":[67],"criterion":[69],"for":[70],"gluing":[72,103],"multipath":[75],"given":[78,108],"to":[80,106,117],"preserve":[81],"$\\mathcal{AO}$-Hamiltonicity.":[82],"Building":[83],"towards":[84],"an":[85],"inductive":[86],"certification":[87],"$\\mathcal{AO}$-Hamiltonicity":[89],"via":[90],"(open)":[92],"ear":[93],"decomposition":[94],"2-connected":[96],"graphs,":[97],"propose":[99],"three":[100],"ways":[101],"several":[104],"graph.":[109],"addition,":[111],"define":[113],"polynomials":[116],"encapsulate":[118],"both":[119],"number":[121],"\"parity":[130],"problem\"":[131],"proposed":[132],"by":[133],"Savage,":[134],"Squire":[135],"West:":[137],"$-1$":[139],"is":[140,152],"not":[141,153,167],"root":[143],"polynomial":[147],"$G$,":[149],"then":[150],"$G$":[151],"explore":[156],"numerous":[157],"properties":[158],"polynomials,":[162,173],"proving":[163],"that":[164,175],"instances":[168],"famous":[171],"Tutte-Whitney":[172],"but":[174],"too":[177],"exhibit":[178],"partial":[180],"deletion-contraction":[181],"phenomenon.":[182]},"counts_by_year":[],"updated_date":"2026-10-28T10:33:24.094632","created_date":"2026-09-04T00:00:00"}
