{"id":"https://openalex.org/W7212113531","doi":"https://doi.org/10.48550/arxiv.2609.09391","title":"On the Hamiltonicity of generating graphs of almost simple groups","display_name":"On the Hamiltonicity of generating graphs of almost simple groups","publication_year":2026,"publication_date":"2026-09-08","ids":{"openalex":"https://openalex.org/W7212113531","doi":"https://doi.org/10.48550/arxiv.2609.09391"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.09391","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.09391","pdf_url":"https://arxiv.org/pdf/2609.09391","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","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.09391","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5116877309","display_name":"Luigi Iorio","orcid":"https://orcid.org/0009-0000-2705-1308","observed_orcids":["https://orcid.org/0009-0000-2705-1308"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Iorio, Luigi","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5116877309"],"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/T10849","display_name":"Finite Group Theory Research","score":1.0,"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/T10849","display_name":"Finite Group Theory Research","score":1.0,"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/T11680","display_name":"Advanced Algebra and Geometry","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"}},{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.0,"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/hamiltonicity","display_name":"Hamiltonicity","score":0.7829999923706055},{"id":"https://openalex.org/keywords/hamiltonian-cycles","display_name":"Hamiltonian cycles","score":0.8479999899864197},{"id":"https://openalex.org/keywords/almost-simple-groups","display_name":"almost simple groups","score":0.9440000057220459},{"id":"https://openalex.org/keywords/finite-groups","display_name":"finite groups","score":0.746999979019165},{"id":"https://openalex.org/keywords/generating-sets","display_name":"generating sets","score":0.39500001072883606},{"id":"https://openalex.org/keywords/asymptotic-results","display_name":"asymptotic results","score":0.40700000524520874}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.864799976348877},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7835999727249146},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.6416000127792358},{"id":"https://openalex.org/C5383885","wikidata":"https://www.wikidata.org/wiki/Q571124","display_name":"Simple group","level":3,"score":0.599399983882904},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.5652999877929688},{"id":"https://openalex.org/C18116961","wikidata":"https://www.wikidata.org/wiki/Q734209","display_name":"Generating set of a group","level":2,"score":0.5364000201225281},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.5131000280380249},{"id":"https://openalex.org/C63388996","wikidata":"https://www.wikidata.org/wiki/Q1340623","display_name":"Classification of finite simple groups","level":4,"score":0.47760000824928284},{"id":"https://openalex.org/C199422724","wikidata":"https://www.wikidata.org/wiki/Q41118","display_name":"Quotient","level":2,"score":0.4650999903678894},{"id":"https://openalex.org/C2993105083","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Simple graph","level":3,"score":0.45329999923706055},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4523000121116638},{"id":"https://openalex.org/C2776306272","wikidata":"https://www.wikidata.org/wiki/Q7553048","display_name":"Socle","level":4,"score":0.40939998626708984},{"id":"https://openalex.org/C2994516854","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Finite graph","level":3,"score":0.4016999900341034},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.3707999885082245},{"id":"https://openalex.org/C20725272","wikidata":"https://www.wikidata.org/wiki/Q245462","display_name":"Cyclic group","level":3,"score":0.36500000953674316},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.3544999957084656},{"id":"https://openalex.org/C2777404646","wikidata":"https://www.wikidata.org/wiki/Q1057968","display_name":"Finite group","level":3,"score":0.3296999931335449},{"id":"https://openalex.org/C128622974","wikidata":"https://www.wikidata.org/wiki/Q849512","display_name":"Symmetric group","level":2,"score":0.31790000200271606},{"id":"https://openalex.org/C162392398","wikidata":"https://www.wikidata.org/wiki/Q272404","display_name":"Finite set","level":2,"score":0.28450000286102295},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.2802000045776367},{"id":"https://openalex.org/C86524685","wikidata":"https://www.wikidata.org/wiki/Q273037","display_name":"Hamiltonian path","level":3,"score":0.2711000144481659},{"id":"https://openalex.org/C81651864","wikidata":"https://www.wikidata.org/wiki/Q874429","display_name":"Group theory","level":2,"score":0.27000001072883606},{"id":"https://openalex.org/C146380142","wikidata":"https://www.wikidata.org/wiki/Q1137726","display_name":"Directed graph","level":2,"score":0.26750001311302185}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.09391","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.09391","pdf_url":"https://arxiv.org/pdf/2609.09391","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.2609.09391","doi":"https://doi.org/10.48550/arxiv.2609.09391","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.09391","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":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.09391","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.09391","pdf_url":"https://arxiv.org/pdf/2609.09391","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":[{"id":"https://openalex.org/F4320311030","display_name":"Istituto Nazionale di Alta Matematica \"Francesco Severi\"","ror":"https://ror.org/01vx64p53"},{"id":"https://openalex.org/F4320334045","display_name":"Gruppo Nazionale per le Strutture Algebriche, Geometriche e le loro Applicazioni","ror":"https://ror.org/00b9dvn87"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7212113531.pdf","grobid_xml":"https://content.openalex.org/works/W7212113531.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2121777536","https://openalex.org/W7110684859","https://openalex.org/W2067167721","https://openalex.org/W2789255310","https://openalex.org/W2524717337","https://openalex.org/W2114080680","https://openalex.org/W1645198615","https://openalex.org/W7099778390","https://openalex.org/W1765056582","https://openalex.org/W2570173166"],"abstract_inverted_index":{"The":[0],"generating":[1],"graph":[2],"$\u0393(G)$":[3,51],"of":[4,63,113],"a":[5,53],"finite":[6,43],"group":[7,44],"$G$":[8,45,64],"has":[9],"vertex":[10],"set":[11],"$G\\setminus\\{1\\}$,":[12],"and":[13,20,30,57,80],"two":[14],"distinct":[15],"vertices":[16],"are":[17],"adjacent":[18],"if":[19,22,56,59],"only":[21,58],"they":[23],"generate":[24],"$G$.":[25],"Breuer,":[26],"Guralnick,":[27],"Lucchini,":[28],"Maroti":[29],"Nagy":[31],"[Bull.":[32],"Lond.":[33],"Math.":[34],"Soc.":[35],"42":[36],"(2010),":[37],"621--633]":[38],"conjectured":[39],"that,":[40],"for":[41,71,81,97,105],"every":[42,60],"with":[46,77,86,111],"at":[47],"least":[48],"four":[49],"elements,":[50],"contains":[52],"Hamiltonian":[54],"cycle":[55],"proper":[61],"quotient":[62],"is":[65],"cyclic.":[66],"They":[67],"proved":[68],"their":[69],"conjecture":[70,104],"sufficiently":[72,106],"large":[73,107],"almost":[74,83,98,108],"simple":[75,84,99,109],"groups":[76,85,100,110],"alternating":[78],"socle":[79,112],"all":[82],"sporadic":[87],"socle.":[88],"In":[89],"this":[90],"paper,":[91],"we":[92],"complete":[93],"the":[94,103],"asymptotic":[95],"picture":[96],"by":[101],"proving":[102],"Lie":[114],"type.":[115]},"counts_by_year":[],"updated_date":"2026-10-28T10:33:24.094632","created_date":"2026-09-11T00:00:00"}
