{"id":"https://openalex.org/W7208835965","doi":"https://doi.org/10.5281/zenodo.22315251","title":"A tree characterization one vertex above the Bougard-Joret counterexample boundary","display_name":"A tree characterization one vertex above the Bougard-Joret counterexample boundary","publication_year":2026,"publication_date":"2026-09-04","ids":{"openalex":"https://openalex.org/W7208835965","doi":"https://doi.org/10.5281/zenodo.22315251"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.22315251","doi":"https://doi.org/10.5281/zenodo.22315251","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.22315251","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","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.5281/zenodo.22315251","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":1,"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":0.8057000041007996,"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":0.8057000041007996,"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":0.1712999939918518,"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/T11476","display_name":"Graph theory and applications","score":0.008200000040233135,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/independence-number","display_name":"independence number","score":0.7070000171661377},{"id":"https://openalex.org/keywords/k-connected-graphs","display_name":"k-connected graphs","score":0.9269999861717224},{"id":"https://openalex.org/keywords/extremal-graph-theory","display_name":"extremal graph theory","score":0.8349999785423279},{"id":"https://openalex.org/keywords/harary-graphs","display_name":"Harary graphs","score":0.9179999828338623},{"id":"https://openalex.org/keywords/graph-connectivity","display_name":"graph connectivity","score":0.40799999237060547}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7824000120162964},{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.6976000070571899},{"id":"https://openalex.org/C128107574","wikidata":"https://www.wikidata.org/wiki/Q182003","display_name":"Injective function","level":2,"score":0.6692000031471252},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6496000289916992},{"id":"https://openalex.org/C2780428219","wikidata":"https://www.wikidata.org/wiki/Q16952335","display_name":"Cover (algebra)","level":2,"score":0.5443000197410583},{"id":"https://openalex.org/C112313634","wikidata":"https://www.wikidata.org/wiki/Q7886648","display_name":"Complement (music)","level":5,"score":0.5263000130653381},{"id":"https://openalex.org/C2780841128","wikidata":"https://www.wikidata.org/wiki/Q5073781","display_name":"Characterization (materials science)","level":2,"score":0.5054000020027161},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4787999987602234},{"id":"https://openalex.org/C2984853995","wikidata":"https://www.wikidata.org/wiki/Q1060343","display_name":"Independence number","level":3,"score":0.47209998965263367},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4147000014781952},{"id":"https://openalex.org/C35651441","wikidata":"https://www.wikidata.org/wiki/Q625303","display_name":"Independence (probability theory)","level":2,"score":0.3953000009059906},{"id":"https://openalex.org/C2777151079","wikidata":"https://www.wikidata.org/wiki/Q141160","display_name":"Parity (physics)","level":2,"score":0.39320001006126404},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.3930000066757202},{"id":"https://openalex.org/C137618395","wikidata":"https://www.wikidata.org/wiki/Q576728","display_name":"Winding number","level":2,"score":0.34200000762939453},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.328900009393692},{"id":"https://openalex.org/C2987642246","wikidata":"https://www.wikidata.org/wiki/Q5452196","display_name":"First order","level":2,"score":0.3125},{"id":"https://openalex.org/C88230418","wikidata":"https://www.wikidata.org/wiki/Q131476","display_name":"Graph theory","level":2,"score":0.304500013589859},{"id":"https://openalex.org/C2777724877","wikidata":"https://www.wikidata.org/wiki/Q2548661","display_name":"Crossing number (knot theory)","level":3,"score":0.2888999879360199},{"id":"https://openalex.org/C48659774","wikidata":"https://www.wikidata.org/wiki/Q4907197","display_name":"Bijection, injection and surjection","level":3,"score":0.28459998965263367},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.28439998626708984},{"id":"https://openalex.org/C162329640","wikidata":"https://www.wikidata.org/wiki/Q332648","display_name":"Covering space","level":2,"score":0.2809000015258789},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.2599000036716461},{"id":"https://openalex.org/C125080357","wikidata":"https://www.wikidata.org/wiki/Q45715","display_name":"Complete graph","level":3,"score":0.25769999623298645}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.5281/zenodo.22315251","doi":"https://doi.org/10.5281/zenodo.22315251","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.22315251","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":null,"raw_source_name":null,"raw_type":"Preprint"},{"id":"doi:10.5281/zenodo.22315252","doi":"https://doi.org/10.5281/zenodo.22315252","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.22315252","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":null,"raw_source_name":null,"raw_type":"Preprint"},{"id":"doi:10.5281/zenodo.22341644","doi":"https://doi.org/10.5281/zenodo.22341644","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.22341644","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":null,"raw_source_name":null,"raw_type":"Preprint"},{"id":"doi:10.5281/zenodo.22823417","doi":"https://doi.org/10.5281/zenodo.22823417","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.22823417","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":null,"raw_source_name":null,"raw_type":"Preprint"},{"id":"doi:10.5281/zenodo.22835072","doi":"https://doi.org/10.5281/zenodo.22835072","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.22835072","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":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.5281/zenodo.22315251","doi":"https://doi.org/10.5281/zenodo.22315251","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.22315251","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":[],"sustainable_development_goals_aurora":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":3,"referenced_works":["https://openalex.org/W2125993726","https://openalex.org/W2334980951","https://openalex.org/W7203861401"],"related_works":[],"abstract_inverted_index":{"Let":[0],"f(n,":[1],"\u03b1,":[2,51],"k)":[3,52],"be":[4],"the":[5,24,33,40,121,145,155],"minimum":[6],"size":[7],"of":[8,12,110,112,114,144],"a":[9],"k-connected":[10],"graph":[11],"order":[13],"n":[14,26],"and":[15,20,31,64,81,119,147,166,174],"independence":[16],"number":[17],"\u03b1.":[18],"Das":[19],"Gupta":[21],"recently":[22],"determined":[23],"boundary":[25],"=":[27,53,106,127],"\u03b1":[28,67,105,126],"+":[29,47,49,55,57,70],"k":[30,48,56,61,69,128],"disproved":[32],"proposed":[34],"Bougard-Joret":[35],"formula":[36],"there.":[37],"We":[38,100],"determine":[39],"entire":[41],"admissible":[42],"first":[43,164],"interior":[44],"shell:":[45],"f(\u03b1":[46],"1,":[50],"\u2308k(\u03b1":[54],"1)/2\u2309":[58],"for":[59],"every":[60],"\u2265":[62],"3":[63],"2":[65,107],"\u2264":[66,68],"1.":[71,130],"The":[72,131,150,161],"construction":[73],"augments":[74],"classical":[75],"Harary":[76],"graphs":[77],"with":[78],"complement":[79],"matchings":[80],"attaches":[82],"an":[83,141],"independent":[84,142],"set":[85],"through":[86],"distinct":[87],"missing-neighbor":[88],"pairs.":[89],"An":[90],"elementary":[91],"cyclic-gap":[92],"proof":[93],"controls":[94],"connectivity,":[95],"including":[96],"all":[97,102],"parity":[98],"cases.":[99],"characterize":[101],"extremizers":[103],"when":[104,125],"as":[108],"complements":[109],"unions":[111],"cycles":[113],"lengths":[115],"at":[116],"least":[117],"five,":[118],"give":[120],"complete":[122],"nonstar-tree":[123],"characterization":[124],"-":[129],"full-shell":[132],"result":[133],"is":[134],"supported":[135],"by":[136],"75":[137],"exact":[138],"finite":[139,159],"constructions,":[140],"re-implementation":[143],"checks,":[146],"negative":[148],"controls.":[149],"universal":[151],"statement":[152],"follows":[153],"from":[154,158],"proof,":[156],"not":[157],"computation.":[160],"general":[162],"revised":[163],"regime":[165,168],"second":[167],"remain":[169],"unresolved.":[170],"Source":[171],"code,":[172],"data":[173],"computational":[175],"records:":[176],"https://github.com/fsantibanezleal/CAOS_RESEARCH":[177],"(problems/combinatorics/bougard-joret).":[178]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-10-08T09:06:37.294493","created_date":"2026-09-06T00:00:00"}