{"id":"https://openalex.org/W2149370230","doi":"https://doi.org/10.1137/0206046","title":"Determining the Stability Number of a Graph","display_name":"Determining the Stability Number of a Graph","publication_year":1977,"publication_date":"1977-12-01","ids":{"openalex":"https://openalex.org/W2149370230","doi":"https://doi.org/10.1137/0206046","mag":"2149370230"},"language":"en","primary_location":{"id":"doi:10.1137/0206046","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0206046","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5111486123","display_name":"Va\u0161ek Chv\u00e1tal","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"V. Chv\u00e1tal","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5111486123"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":5.5241,"has_fulltext":false,"cited_by_count":52,"citation_normalized_percentile":{"value":0.9668481,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"6","issue":"4","first_page":"643","last_page":"662"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9998000264167786,"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":0.9998000264167786,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.996999979019165,"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/T12292","display_name":"Graph Theory and Algorithms","score":0.9959999918937683,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/mathematical-proof","display_name":"Mathematical proof","score":0.7941959500312805},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6483115553855896},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6233634352684021},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5449863076210022},{"id":"https://openalex.org/keywords/clique","display_name":"Clique","score":0.5056393146514893},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.461175799369812},{"id":"https://openalex.org/keywords/split-graph","display_name":"Split graph","score":0.4524669349193573},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.4191458821296692},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.2609426975250244},{"id":"https://openalex.org/keywords/pathwidth","display_name":"Pathwidth","score":0.23548623919487}],"concepts":[{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.7941959500312805},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6483115553855896},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6233634352684021},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5449863076210022},{"id":"https://openalex.org/C2777035058","wikidata":"https://www.wikidata.org/wiki/Q1662634","display_name":"Clique","level":2,"score":0.5056393146514893},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.461175799369812},{"id":"https://openalex.org/C8554925","wikidata":"https://www.wikidata.org/wiki/Q3893853","display_name":"Split graph","level":5,"score":0.4524669349193573},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4191458821296692},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.2609426975250244},{"id":"https://openalex.org/C43517604","wikidata":"https://www.wikidata.org/wiki/Q7144893","display_name":"Pathwidth","level":4,"score":0.23548623919487},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/0206046","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0206046","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Computing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W1655990431","https://openalex.org/W2007200873","https://openalex.org/W2024527820","https://openalex.org/W2045472305","https://openalex.org/W2091593479","https://openalex.org/W2097844290","https://openalex.org/W2112575355","https://openalex.org/W2127813745","https://openalex.org/W2138163102","https://openalex.org/W2146162554","https://openalex.org/W2401610261","https://openalex.org/W4238472918","https://openalex.org/W4312512934"],"related_works":["https://openalex.org/W2808944898","https://openalex.org/W4254119641","https://openalex.org/W3196207352","https://openalex.org/W2951724202","https://openalex.org/W3084261076","https://openalex.org/W4387820098","https://openalex.org/W2576399385","https://openalex.org/W2963408011","https://openalex.org/W2052760902","https://openalex.org/W2109292317"],"abstract_inverted_index":{"We":[0],"formalize":[1],"certain":[2],"rules":[3],"for":[4,37,52],"deriving":[5],"upper":[6],"bounds":[7],"on":[8,35],"the":[9,24,39,43],"stability":[10,40],"number":[11,41,61],"of":[12,26,62],"a":[13,57],"graph.":[14],"The":[15],"resulting":[16],"system":[17,67],"is":[18],"powerful":[19],"enough":[20],"to":[21],"(i)":[22],"encompass":[23],"algorithms":[25],"Tarjan\u2019s":[27],"type":[28],"and":[29],"(ii)":[30],"provide":[31],"very":[32],"short":[33],"proofs":[34,64],"graphs":[36,55],"which":[38],"equals":[42],"clique-covering":[44],"number.":[45],"However,":[46],"our":[47,66],"main":[48],"result":[49],"shows":[50],"that":[51],"almost":[53],"all":[54],"with":[56],"(sufficiently":[58],"large)":[59],"linear":[60],"edges,":[63],"within":[65],"must":[68],"have":[69],"at":[70],"least":[71],"exponential":[72],"length.":[73]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
