{"id":"https://openalex.org/W2152478214","doi":"https://doi.org/10.37236/637","title":"Independence Number and Disjoint Theta Graphs","display_name":"Independence Number and Disjoint Theta Graphs","publication_year":2011,"publication_date":"2011-07-22","ids":{"openalex":"https://openalex.org/W2152478214","doi":"https://doi.org/10.37236/637","mag":"2152478214"},"language":"en","primary_location":{"id":"doi:10.37236/637","is_oa":true,"landing_page_url":"https://doi.org/10.37236/637","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v18i1p150/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v18i1p150/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101970850","display_name":"Shinya Fujita","orcid":"https://orcid.org/0000-0001-8812-8321"},"institutions":[{"id":"https://openalex.org/I4210154076","display_name":"National Institute of Technology, Gunma College","ror":"https://ror.org/04kp2z675","country_code":"JP","type":"education","lineage":["https://openalex.org/I4210120810","https://openalex.org/I4210154076"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Shinya Fujita","raw_affiliation_strings":["Gunma National College of Technology. 580 Toriba, Maebashi, Gunma, Japan 371-8530"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Gunma National College of Technology. 580 Toriba, Maebashi, Gunma, Japan 371-8530","institution_ids":["https://openalex.org/I4210154076"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5059837046","display_name":"Colton Magnant","orcid":"https://orcid.org/0000-0002-3723-798X"},"institutions":[{"id":"https://openalex.org/I39815113","display_name":"Georgia Southern University","ror":"https://ror.org/04agmb972","country_code":"US","type":"education","lineage":["https://openalex.org/I39815113"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Colton Magnant","raw_affiliation_strings":["Georgia Southern University, 65 Georgia Ave. Room 3008, Statesboro, GA 30460, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Georgia Southern University, 65 Georgia Ave. Room 3008, Statesboro, GA 30460, USA","institution_ids":["https://openalex.org/I39815113"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.8959,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.72724439,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"18","issue":"1","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":0.9998000264167786,"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":0.9998000264167786,"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":0.9994000196456909,"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/T11476","display_name":"Graph theory and applications","score":0.9987000226974487,"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/combinatorics","display_name":"Combinatorics","score":0.8931646347045898},{"id":"https://openalex.org/keywords/disjoint-sets","display_name":"Disjoint sets","score":0.8359469175338745},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7895102500915527},{"id":"https://openalex.org/keywords/independence-number","display_name":"Independence number","score":0.7859904766082764},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5304856896400452},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.49009478092193604},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.45980751514434814},{"id":"https://openalex.org/keywords/chordal-graph","display_name":"Chordal graph","score":0.4410734176635742},{"id":"https://openalex.org/keywords/indifference-graph","display_name":"Indifference graph","score":0.42219099402427673},{"id":"https://openalex.org/keywords/cograph","display_name":"Cograph","score":0.41425493359565735},{"id":"https://openalex.org/keywords/1-planar-graph","display_name":"1-planar graph","score":0.24912190437316895}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8931646347045898},{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.8359469175338745},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7895102500915527},{"id":"https://openalex.org/C2984853995","wikidata":"https://www.wikidata.org/wiki/Q1060343","display_name":"Independence number","level":3,"score":0.7859904766082764},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5304856896400452},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.49009478092193604},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.45980751514434814},{"id":"https://openalex.org/C160446614","wikidata":"https://www.wikidata.org/wiki/Q1322892","display_name":"Chordal graph","level":3,"score":0.4410734176635742},{"id":"https://openalex.org/C74133993","wikidata":"https://www.wikidata.org/wiki/Q3115472","display_name":"Indifference graph","level":3,"score":0.42219099402427673},{"id":"https://openalex.org/C59824394","wikidata":"https://www.wikidata.org/wiki/Q5141281","display_name":"Cograph","level":5,"score":0.41425493359565735},{"id":"https://openalex.org/C102192266","wikidata":"https://www.wikidata.org/wiki/Q4545823","display_name":"1-planar graph","level":4,"score":0.24912190437316895}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.37236/637","is_oa":true,"landing_page_url":"https://doi.org/10.37236/637","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v18i1p150/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.1019.129","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.1019.129","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://digitalcommons.georgiasouthern.edu/cgi/viewcontent.cgi?article%3D1103%26context%3Dmath-sci-facpubs","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.372.7742","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.372.7742","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.combinatorics.org/ojs/index.php/eljc/article/viewFile/v18i1p150/pdf/","raw_type":"text"}],"best_oa_location":{"id":"doi:10.37236/637","is_oa":true,"landing_page_url":"https://doi.org/10.37236/637","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v18i1p150/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4148599816","display_name":"A STUDY ON PARTITION PROBLEMS IN HIGHLY CONNECTED GRAPHS AND FORBIDDEN SUBGRAPHS","funder_award_id":"20740068","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"}],"funders":[{"id":"https://openalex.org/F4320334764","display_name":"Japan Society for the Promotion of Science","ror":"https://ror.org/00hhkn466"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2152478214.pdf","grobid_xml":"https://content.openalex.org/works/W2152478214.grobid-xml"},"referenced_works_count":30,"referenced_works":["https://openalex.org/W207973212","https://openalex.org/W1569752386","https://openalex.org/W1604945782","https://openalex.org/W1974181313","https://openalex.org/W1983677868","https://openalex.org/W2001686801","https://openalex.org/W2035570915","https://openalex.org/W2040973492","https://openalex.org/W2041854775","https://openalex.org/W2047313674","https://openalex.org/W2050261129","https://openalex.org/W2052169294","https://openalex.org/W2055130189","https://openalex.org/W2067371453","https://openalex.org/W2076266010","https://openalex.org/W2083044334","https://openalex.org/W2085599660","https://openalex.org/W2091613024","https://openalex.org/W2091699090","https://openalex.org/W2157049835","https://openalex.org/W2612978016","https://openalex.org/W2951660881","https://openalex.org/W4231406198","https://openalex.org/W4249360058","https://openalex.org/W4298414065","https://openalex.org/W6650892939","https://openalex.org/W6663483672","https://openalex.org/W6669550547","https://openalex.org/W6673189935","https://openalex.org/W6764765763"],"related_works":["https://openalex.org/W2083238533","https://openalex.org/W4220852510","https://openalex.org/W2061237693","https://openalex.org/W4385327816","https://openalex.org/W4385588236","https://openalex.org/W3139101777","https://openalex.org/W603403972","https://openalex.org/W2949743119","https://openalex.org/W1811797198","https://openalex.org/W2041783376"],"abstract_inverted_index":{"The":[0],"goal":[1],"of":[2,24,61,92,115],"this":[3,15,51,106],"paper":[4,52],"is":[5],"to":[6,20,35],"find":[7],"vertex":[8],"disjoint":[9,31,74,87],"even":[10,81,88],"cycles":[11,89],"in":[12,50,90],"graphs.":[13,116],"For":[14],"purpose,":[16],"define":[17],"a":[18,22,43,62,109],"$\\theta$-graph":[19,78],"be":[21],"pair":[23],"vertices":[25],"$u,":[26],"v$":[27],"with":[28,64],"three":[29],"internally":[30],"paths":[32],"joining":[33],"$u$":[34],"$v$.":[36],"Given":[37],"an":[38,80],"independence":[39,65],"number":[40,66],"$\\alpha$":[41],"and":[42,108],"fixed":[44],"integer":[45],"$k$,":[46],"the":[47,57,103],"results":[48,84],"contained":[49],"provide":[53,85],"sharp":[54],"bounds":[55],"on":[56],"order":[58,93],"$f(k,":[59,96],"\\alpha)$":[60],"graph":[63],"$\\alpha(G)":[67],"\\leq":[68],"\\alpha$":[69],"which":[70],"contains":[71,79],"no":[72],"$k$":[73,86],"$\\theta$-graphs.":[75],"Since":[76],"every":[77],"cycle,":[82],"these":[83],"graphs":[91],"at":[94],"least":[95],"\\alpha)":[97],"+":[98],"1$.":[99],"We":[100],"also":[101],"discuss":[102],"relationship":[104],"between":[105],"problem":[107,112],"generalized":[110],"ramsey":[111],"involving":[113],"sets":[114]},"counts_by_year":[{"year":2014,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
