{"id":"https://openalex.org/W1987533363","doi":"https://doi.org/10.1137/s0895480194276909","title":"The Ultimate Categorical Independence Ratio of a Graph","display_name":"The Ultimate Categorical Independence Ratio of a Graph","publication_year":1996,"publication_date":"1996-05-01","ids":{"openalex":"https://openalex.org/W1987533363","doi":"https://doi.org/10.1137/s0895480194276909","mag":"1987533363"},"language":"en","primary_location":{"id":"doi:10.1137/s0895480194276909","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895480194276909","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"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 Discrete Mathematics","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/A5045473830","display_name":"Jason I. Brown","orcid":"https://orcid.org/0000-0002-4721-8985"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Jason I. Brown","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5080800191","display_name":"Richard J. Nowakowski","orcid":"https://orcid.org/0000-0002-4434-672X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Richard J. Nowakowski","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5073086838","display_name":"Douglas F. Rall","orcid":"https://orcid.org/0000-0002-5482-756X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Douglas Rall","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5045473830"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":21,"citation_normalized_percentile":{"value":0.1121238,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"9","issue":"2","first_page":"290","last_page":"300"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9990000128746033,"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":0.9990000128746033,"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":0.9990000128746033,"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/T11476","display_name":"Graph theory and applications","score":0.9980000257492065,"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/mathematics","display_name":"Mathematics","score":0.8015209436416626},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7821255326271057},{"id":"https://openalex.org/keywords/independence-number","display_name":"Independence number","score":0.5509624481201172},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5393595099449158},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5252315998077393},{"id":"https://openalex.org/keywords/edge-transitive-graph","display_name":"Edge-transitive graph","score":0.4593108296394348},{"id":"https://openalex.org/keywords/bounding-overwatch","display_name":"Bounding overwatch","score":0.4298152029514313},{"id":"https://openalex.org/keywords/categorical-variable","display_name":"Categorical variable","score":0.42731574177742004},{"id":"https://openalex.org/keywords/graph-power","display_name":"Graph power","score":0.3978785574436188},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.23078513145446777},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.071494460105896}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8015209436416626},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7821255326271057},{"id":"https://openalex.org/C2984853995","wikidata":"https://www.wikidata.org/wiki/Q1060343","display_name":"Independence number","level":3,"score":0.5509624481201172},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5393595099449158},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5252315998077393},{"id":"https://openalex.org/C200597783","wikidata":"https://www.wikidata.org/wiki/Q4391289","display_name":"Edge-transitive graph","level":5,"score":0.4593108296394348},{"id":"https://openalex.org/C63584917","wikidata":"https://www.wikidata.org/wiki/Q333286","display_name":"Bounding overwatch","level":2,"score":0.4298152029514313},{"id":"https://openalex.org/C5274069","wikidata":"https://www.wikidata.org/wiki/Q2285707","display_name":"Categorical variable","level":2,"score":0.42731574177742004},{"id":"https://openalex.org/C149530733","wikidata":"https://www.wikidata.org/wiki/Q5597091","display_name":"Graph power","level":4,"score":0.3978785574436188},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.23078513145446777},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.071494460105896},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/s0895480194276909","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895480194276909","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"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 Discrete Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W753810742","https://openalex.org/W1513353427","https://openalex.org/W1982982957","https://openalex.org/W2008495201","https://openalex.org/W2038488239","https://openalex.org/W2054651287","https://openalex.org/W2067188437","https://openalex.org/W2078289947","https://openalex.org/W2090463147","https://openalex.org/W2095076239","https://openalex.org/W2164684058","https://openalex.org/W2167519573","https://openalex.org/W4388323696"],"related_works":["https://openalex.org/W2394181405","https://openalex.org/W2366402698","https://openalex.org/W2391570583","https://openalex.org/W2791083046","https://openalex.org/W2021553593","https://openalex.org/W2358646185","https://openalex.org/W3104688290","https://openalex.org/W2370823119","https://openalex.org/W2237046474","https://openalex.org/W2531609948"],"abstract_inverted_index":{"Let":[0],"$\\beta":[1],"(G)$":[2],"denote":[3],"the":[4,26,37,111],"independence":[5],"number":[6],"of":[7,131],"a":[8,93,128,139,148],"graph":[9,28,130,141],"G.":[10,90],"We":[11,46,91],"introduce":[12],"$A(G)":[13,102,117],"=":[14,118],"\\lim_{k":[15],"\\to":[16],"\\infty":[17],"}":[18],"\\beta":[19,104,119],"(G^k":[20],")/|":[21],"V(G)":[22,106,121],"|^k":[23],"$,":[24],"where":[25],"categorical":[27],"product":[29],"is":[30,59,66,74,127,138],"used.":[31],"This":[32,108,123],"limit,":[33],"surprisingly,":[34],"lies":[35],"in":[36],"range":[38],"$(":[39],"0,1/2":[40],"]":[41],"\\cup":[42],"\\{":[43],"1":[44],"\\}$.":[45],"can":[47,52],"show":[48],"that":[49,101,142],"this":[50],"limit":[51],"take":[53],"any":[54,61],"such":[55],"rational":[56],"number,":[57],"but":[58],"there":[60],"G":[62,99,115,126,137],"for":[63,71,88,98,113],"which":[64,95,114,146],"$A(G)$":[65,73,87],"irrational?":[67],"A":[68],"useful":[69],"technique":[70],"bounding":[72],"to":[75,84],"consider":[76],"special":[77],"spanning":[78],"subgraphs.":[79],"These":[80],"bounds":[81],"allow":[82],"us":[83],"efficiently":[85],"compute":[86],"many":[89],"give":[92],"condition":[94],"if":[96,125,136],"true":[97],"shows":[100],">":[103],"(G)/|":[105,120],"|$.":[107],"brings":[109],"up":[110],"question;":[112],"does":[116],"|$?":[122],"happens":[124],"Cayley":[129],"an":[132,144],"Abelian":[133],"group":[134],"or":[135],"connected":[140],"has":[143,147],"automorphism":[145],"single":[149],"orbit.":[150]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
