{"id":"https://openalex.org/W7216501024","doi":"https://doi.org/10.48550/arxiv.2610.00144","title":"Probability threshold for the stability of $\u03b1(G(n,r,s))$","display_name":"Probability threshold for the stability of $\u03b1(G(n,r,s))$","publication_year":2026,"publication_date":"2026-09-10","ids":{"openalex":"https://openalex.org/W7216501024","doi":"https://doi.org/10.48550/arxiv.2610.00144"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.00144","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.00144","pdf_url":"https://arxiv.org/pdf/2610.00144","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/2610.00144","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5155546036","display_name":"M. M. Koshelev","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Koshelev, M. M.","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5155813219","display_name":"A. M. Raigorodskii","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Raigorodskii, A. M.","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":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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9990000128746033,"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":0.9990000128746033,"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.00039999998989515007,"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":0.00019999999494757503,"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":0.6449999809265137},{"id":"https://openalex.org/keywords/threshold-probability","display_name":"threshold probability","score":0.7319999933242798},{"id":"https://openalex.org/keywords/kneser-graphs","display_name":"Kneser graphs","score":0.7950000166893005},{"id":"https://openalex.org/keywords/random-hypergraphs","display_name":"random hypergraphs","score":0.6159999966621399},{"id":"https://openalex.org/keywords/asymptotic-stability","display_name":"asymptotic stability","score":0.6290000081062317},{"id":"https://openalex.org/keywords/extremal-graph-theory","display_name":"extremal graph theory","score":0.5830000042915344}],"concepts":[{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.7200999855995178},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6980999708175659},{"id":"https://openalex.org/C35651441","wikidata":"https://www.wikidata.org/wiki/Q625303","display_name":"Independence (probability theory)","level":2,"score":0.633400022983551},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4645000100135803},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4203999936580658},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.3549000024795532},{"id":"https://openalex.org/C167964875","wikidata":"https://www.wikidata.org/wiki/Q17011487","display_name":"Exponential stability","level":3,"score":0.35359999537467957},{"id":"https://openalex.org/C122203268","wikidata":"https://www.wikidata.org/wiki/Q5862903","display_name":"Probability theory","level":2,"score":0.35040000081062317},{"id":"https://openalex.org/C197055811","wikidata":"https://www.wikidata.org/wiki/Q207522","display_name":"Probability density function","level":2,"score":0.3440000116825104},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.28929999470710754},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.2840000092983246},{"id":"https://openalex.org/C21031990","wikidata":"https://www.wikidata.org/wiki/Q355020","display_name":"Probability measure","level":2,"score":0.2818000018596649},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.2791000008583069},{"id":"https://openalex.org/C2778925954","wikidata":"https://www.wikidata.org/wiki/Q16883749","display_name":"Stability criterion","level":3,"score":0.266400009393692},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.2506999969482422}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.00144","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.00144","pdf_url":"https://arxiv.org/pdf/2610.00144","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.2610.00144","doi":"https://doi.org/10.48550/arxiv.2610.00144","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.00144","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","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":"pmh:oai:arXiv.org:2610.00144","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.00144","pdf_url":"https://arxiv.org/pdf/2610.00144","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/W7216501024.pdf","grobid_xml":"https://content.openalex.org/works/W7216501024.grobid-xml"},"referenced_works_count":17,"referenced_works":["https://openalex.org/W1992844673","https://openalex.org/W2025324955","https://openalex.org/W2031983827","https://openalex.org/W2102524299","https://openalex.org/W2153305111","https://openalex.org/W2263134931","https://openalex.org/W2291404673","https://openalex.org/W2291857129","https://openalex.org/W2297392811","https://openalex.org/W2516050763","https://openalex.org/W2609217482","https://openalex.org/W3156461825","https://openalex.org/W3167180680","https://openalex.org/W3214004568","https://openalex.org/W4210761435","https://openalex.org/W7128731627","https://openalex.org/W7212069088"],"related_works":["https://openalex.org/W4416057644","https://openalex.org/W3214004568","https://openalex.org/W2971253552","https://openalex.org/W4213429878","https://openalex.org/W2782277821","https://openalex.org/W7221809599","https://openalex.org/W2235209920","https://openalex.org/W7212069088","https://openalex.org/W3121773111","https://openalex.org/W2238499597"],"abstract_inverted_index":{"Let":[0],"$G(n,r,s)$":[1],"be":[2],"a":[3],"graph":[4],"$(V,E)$":[5],"such":[6],"that":[7,52],"$V":[8],"=":[9,13,19],"\\binom{[n]}{r}$":[10],"and":[11],"$E":[12],"\\{(u,":[14],"v)|":[15],"|u":[16],"\\cap":[17],"v|":[18],"s\\}.":[20],"$In":[21],"this":[22],"paper":[23],"we":[24],"study":[25],"the":[26,30,34,47,57],"probability":[27],"threshold":[28],"for":[29],"exact":[31],"stability":[32,55],"of":[33,37,50,56],"independence":[35,58],"number":[36],"$G(n,":[38],"r,":[39],"s)$":[40],"where":[41],"$r":[42],">":[43],"2s+2$.":[44],"We":[45],"improve":[46],"previous":[48],"result":[49],"Pyaderkin":[51],"implied":[53],"asymptotic":[54],"number.":[59]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-03T00:00:00"}