{"id":"https://openalex.org/W7225455976","doi":"https://doi.org/10.5281/zenodo.24044537","title":"Exact values of the Bougard-Joret function in its open second regime up to order 22","display_name":"Exact values of the Bougard-Joret function in its open second regime up to order 22","publication_year":2026,"publication_date":"2026-11-07","ids":{"openalex":"https://openalex.org/W7225455976","doi":"https://doi.org/10.5281/zenodo.24044537"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.24044537","doi":"https://doi.org/10.5281/zenodo.24044537","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24044537","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.5281/zenodo.24044537","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5057549475","display_name":"Felipe A. Santib\u00e1\u00f1ez-Leal","orcid":"https://orcid.org/0000-0002-0150-3246","observed_orcids":["https://orcid.org/0000-0002-0150-3246"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Santib\u00e1\u00f1ez-Leal, Felipe","raw_affiliation_strings":["CAOS open-research programme, Santiago, Chile"],"raw_orcid":"https://orcid.org/0000-0002-0150-3246","affiliations":[{"raw_affiliation_string":"CAOS open-research programme, Santiago, Chile","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5057549475"],"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/T10374","display_name":"Advanced Graph Theory Research","score":0.888700008392334,"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"}},"topics":[{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.888700008392334,"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":0.08139999955892563,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.016300000250339508,"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/independence-number","display_name":"independence number","score":0.6930000185966492},{"id":"https://openalex.org/keywords/k-connected-graphs","display_name":"k-connected graphs","score":0.9470000267028809},{"id":"https://openalex.org/keywords/extremal-graph-theory","display_name":"extremal graph theory","score":0.8429999947547913},{"id":"https://openalex.org/keywords/graph-enumeration","display_name":"graph enumeration","score":0.6110000014305115},{"id":"https://openalex.org/keywords/exact-enumeration","display_name":"exact enumeration","score":0.41999998688697815},{"id":"https://openalex.org/keywords/pruning-rules","display_name":"pruning rules","score":0.6150000095367432},{"id":"https://openalex.org/keywords/nauty","display_name":"nauty","score":0.48899999260902405},{"id":"https://openalex.org/keywords/extremal-graphs","display_name":"extremal graphs","score":0.48399999737739563}],"concepts":[{"id":"https://openalex.org/C156340839","wikidata":"https://www.wikidata.org/wiki/Q2704791","display_name":"Enumeration","level":2,"score":0.8540999889373779},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8396000266075134},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7626000046730042},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.742900013923645},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5169000029563904},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5084999799728394},{"id":"https://openalex.org/C2984853995","wikidata":"https://www.wikidata.org/wiki/Q1060343","display_name":"Independence number","level":3,"score":0.48489999771118164},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.4749999940395355},{"id":"https://openalex.org/C106131492","wikidata":"https://www.wikidata.org/wiki/Q3072260","display_name":"Filter (signal processing)","level":2,"score":0.4440999925136566},{"id":"https://openalex.org/C75432250","wikidata":"https://www.wikidata.org/wiki/Q29654355","display_name":"Real line","level":2,"score":0.39809998869895935},{"id":"https://openalex.org/C88230418","wikidata":"https://www.wikidata.org/wiki/Q131476","display_name":"Graph theory","level":2,"score":0.361299991607666},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.3546000123023987},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.3529999852180481},{"id":"https://openalex.org/C198352243","wikidata":"https://www.wikidata.org/wiki/Q37105","display_name":"Line (geometry)","level":2,"score":0.35040000081062317},{"id":"https://openalex.org/C204911207","wikidata":"https://www.wikidata.org/wiki/Q860609","display_name":"Generating function","level":2,"score":0.31380000710487366},{"id":"https://openalex.org/C2776291640","wikidata":"https://www.wikidata.org/wiki/Q2912517","display_name":"Value (mathematics)","level":2,"score":0.2874999940395355},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.2680000066757202},{"id":"https://openalex.org/C125080357","wikidata":"https://www.wikidata.org/wiki/Q45715","display_name":"Complete graph","level":3,"score":0.2662000060081482},{"id":"https://openalex.org/C146380142","wikidata":"https://www.wikidata.org/wiki/Q1137726","display_name":"Directed graph","level":2,"score":0.26420000195503235},{"id":"https://openalex.org/C76444178","wikidata":"https://www.wikidata.org/wiki/Q72897900","display_name":"Connectivity","level":3,"score":0.2615000009536743},{"id":"https://openalex.org/C35651441","wikidata":"https://www.wikidata.org/wiki/Q625303","display_name":"Independence (probability theory)","level":2,"score":0.26089999079704285},{"id":"https://openalex.org/C108010975","wikidata":"https://www.wikidata.org/wiki/Q500094","display_name":"Pruning","level":2,"score":0.25870001316070557},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.25110000371932983}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.5281/zenodo.24044537","doi":"https://doi.org/10.5281/zenodo.24044537","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24044537","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},{"id":"doi:10.5281/zenodo.24044538","doi":"https://doi.org/10.5281/zenodo.24044538","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24044538","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},{"id":"doi:10.5281/zenodo.24059677","doi":"https://doi.org/10.5281/zenodo.24059677","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24059677","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.5281/zenodo.24044537","doi":"https://doi.org/10.5281/zenodo.24044537","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24044537","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","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":5,"referenced_works":["https://openalex.org/W1990600049","https://openalex.org/W2334980951","https://openalex.org/W7203861401","https://openalex.org/W7208806833","https://openalex.org/W7208835965"],"related_works":["https://openalex.org/W7203861401","https://openalex.org/W7208835965","https://openalex.org/W2328101025","https://openalex.org/W2398841770","https://openalex.org/W1964774918","https://openalex.org/W3006344862","https://openalex.org/W7095249383","https://openalex.org/W7097522771","https://openalex.org/W2143386956","https://openalex.org/W2020999819"],"abstract_inverted_index":{"Let":[0],"f(n,":[1,25],"\u03b1,":[2,26],"k)":[3,27],"be":[4],"the":[5,41,44,54,58,70,114,117,158,162,179,194],"minimum":[6],"number":[7,19],"of":[8,10,14,43,47,57,112,123,161,183],"edges":[9],"a":[11],"k-connected":[12],"graph":[13,126],"order":[15,184],"n":[16,34,104],"with":[17,96,138],"independence":[18],"\u03b1.":[20],"Bougard":[21,66],"and":[22,51,60,67,103,146,193],"Joret":[23,68],"conjectured":[24,118],"=":[28],"t(n,":[29,38],"\u03b1)":[30,39],"+":[31,80],"\u2308k\u03b1/2\u2309":[32,77],"when":[33,74],">":[35],"k\u03b1,":[36],"where":[37],"is":[40],"size":[42],"balanced":[45],"union":[46],"\u03b1":[48,79,83,97],"cliques.":[49],"Das":[50],"Gupta":[52],"disproved":[53],"other":[55],"line":[56,72,160],"conjecture":[59,163],"left":[61],"this":[62],"second":[63,71,159],"regime":[64],"open.":[65],"proved":[69,144],"only":[73],"\u230an/\u03b1\u230b":[75],"\u2265":[76,84,98,101],"\u2212":[78],"2":[81],"(for":[82],"3).":[85],"We":[86],"compute":[87],"f":[88],"exactly":[89],"at":[90],"every":[91,110,124],"triple":[92],"outside":[93],"that":[94,142],"range":[95],"3,":[99],"k":[100],"3":[102],"\u2264":[105],"23:":[106],"47":[107],"triples.":[108],"At":[109],"one":[111],"them":[113],"value":[115],"equals":[116],"one,":[119],"by":[120],"complete":[121],"enumeration":[122,135,191],"candidate":[125,130,187],"below":[127],"it":[128,173],"(6,224,502,963":[129],"graphs":[131],"in":[132,164,174],"all).":[133],"The":[134,155],"uses":[136],"nauty":[137],"two":[139],"pruning":[140],"rules":[141],"are":[143],"sound,":[145],"an":[147,152],"exact":[148],"filter":[149],"checked":[150],"against":[151],"independent":[153],"implementation.":[154],"data":[156],"support":[157],"its":[165],"smallest":[166],"open":[167,181],"cases;":[168],"they":[169],"do":[170],"not":[171],"prove":[172],"general.":[175],"Version":[176],"0.02":[177],"adds":[178],"eight":[180],"triples":[182],"23":[185],"(7,304,488":[186],"graphs).":[188],"Source":[189],"code,":[190],"records":[192],"extremal":[195],"graphs:":[196],"https://github.com/fsantibanezleal/CAOS_RESEARCH":[197],"(problems/combinatorics/bougard-joret,":[198],"experiments":[199],"EXP-005":[200],"to":[201],"EXP-008).":[202]},"counts_by_year":[],"updated_date":"2026-11-11T12:16:26.678958","created_date":"2026-11-08T00:00:00"}
