{"id":"https://openalex.org/W2170803232","doi":"https://doi.org/10.1002/jgt.3190190313","title":"The fractional chromatic number of mycielski's graphs","display_name":"The fractional chromatic number of mycielski's graphs","publication_year":1995,"publication_date":"1995-05-01","ids":{"openalex":"https://openalex.org/W2170803232","doi":"https://doi.org/10.1002/jgt.3190190313","mag":"2170803232"},"language":"en","primary_location":{"id":"doi:10.1002/jgt.3190190313","is_oa":false,"landing_page_url":"https://doi.org/10.1002/jgt.3190190313","pdf_url":null,"source":{"id":"https://openalex.org/S193368155","display_name":"Journal of Graph Theory","issn_l":"0364-9024","issn":["0364-9024","1097-0118"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Graph Theory","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/A5035231652","display_name":"Michael Larsen","orcid":"https://orcid.org/0000-0002-6680-2730"},"institutions":[{"id":"https://openalex.org/I79576946","display_name":"University of Pennsylvania","ror":"https://ror.org/00b30xv10","country_code":"US","type":"education","lineage":["https://openalex.org/I79576946"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Michael Larsen","raw_affiliation_strings":["University of Pennsylvania Philadelphia, Pennsylvania"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Pennsylvania Philadelphia, Pennsylvania","institution_ids":["https://openalex.org/I79576946"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5032538374","display_name":"James Propp","orcid":null},"institutions":[{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"James Propp","raw_affiliation_strings":["Massachusetts Institute of Technology Cambridge, Massachusetts"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Massachusetts Institute of Technology Cambridge, Massachusetts","institution_ids":["https://openalex.org/I63966007"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5070211483","display_name":"Daniel H. Ullman","orcid":null},"institutions":[{"id":"https://openalex.org/I193531525","display_name":"George Washington University","ror":"https://ror.org/00y4zzh67","country_code":"US","type":"education","lineage":["https://openalex.org/I193531525"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Daniel Ullman","raw_affiliation_strings":["George Washington University Washington, DC"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"George Washington University Washington, DC","institution_ids":["https://openalex.org/I193531525"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":3760,"currency":"USD","value_usd":3760},"apc_paid":null,"fwci":5.3113,"has_fulltext":false,"cited_by_count":94,"citation_normalized_percentile":{"value":0.96355556,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"19","issue":"3","first_page":"411","last_page":"416"},"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":0.9994999766349792,"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":0.9994999766349792,"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/T12536","display_name":"Topological and Geometric Data Analysis","score":0.9976999759674072,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9940000176429749,"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/combinatorics","display_name":"Combinatorics","score":0.8758446574211121},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7873126864433289},{"id":"https://openalex.org/keywords/chromatic-scale","display_name":"Chromatic scale","score":0.7665215730667114},{"id":"https://openalex.org/keywords/clique-number","display_name":"Clique number","score":0.6419032216072083},{"id":"https://openalex.org/keywords/clique","display_name":"Clique","score":0.5785760879516602},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.5591852068901062},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4584275484085083}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8758446574211121},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7873126864433289},{"id":"https://openalex.org/C196956537","wikidata":"https://www.wikidata.org/wiki/Q202021","display_name":"Chromatic scale","level":2,"score":0.7665215730667114},{"id":"https://openalex.org/C2985491264","wikidata":"https://www.wikidata.org/wiki/Q761631","display_name":"Clique number","level":3,"score":0.6419032216072083},{"id":"https://openalex.org/C2777035058","wikidata":"https://www.wikidata.org/wiki/Q1662634","display_name":"Clique","level":2,"score":0.5785760879516602},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.5591852068901062},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4584275484085083},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1002/jgt.3190190313","is_oa":false,"landing_page_url":"https://doi.org/10.1002/jgt.3190190313","pdf_url":null,"source":{"id":"https://openalex.org/S193368155","display_name":"Journal of Graph Theory","issn_l":"0364-9024","issn":["0364-9024","1097-0118"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Graph Theory","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320309515","display_name":"George Washington University","ror":"https://ror.org/00y4zzh67"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W753810742","https://openalex.org/W1511234378","https://openalex.org/W2003995429","https://openalex.org/W2011772662","https://openalex.org/W2027438813","https://openalex.org/W2033050904","https://openalex.org/W2037296716","https://openalex.org/W2040734438","https://openalex.org/W2054651287","https://openalex.org/W2078289947","https://openalex.org/W2126517143","https://openalex.org/W2164684058","https://openalex.org/W2327808709","https://openalex.org/W4210698998","https://openalex.org/W4246380588","https://openalex.org/W6622256421","https://openalex.org/W6657271503"],"related_works":["https://openalex.org/W2781377992","https://openalex.org/W300955832","https://openalex.org/W190087469","https://openalex.org/W3026920247","https://openalex.org/W1644688562","https://openalex.org/W2984191194","https://openalex.org/W2982077839","https://openalex.org/W3145951188","https://openalex.org/W2074614998","https://openalex.org/W1992504234"],"abstract_inverted_index":{"Abstract":[0],"James":[1],"Propp":[2],"The":[3],"most":[4],"familiar":[5],"construction":[6],"of":[7,29,49,57],"graphs":[8,31],"whose":[9],"clique":[10],"number":[11,18,48],"is":[12,19],"much":[13],"smaller":[14],"than":[15],"their":[16],"chromatic":[17,47],"due":[20],"to":[21],"Mycielski,":[22],"who":[23],"constructed":[24],"a":[25,63,66,70],"sequence":[26,56],"G":[27,34,50],"n":[28,35,38,51,67,71],"triangle\u2010free":[30],"with":[32],"X(":[33],")":[36],"=":[37,65],".":[39],"In":[40],"this":[41,55],"article,":[42],"we":[43],"calculate":[44],"the":[45,60],"fractional":[46],"and":[52],"show":[53],"that":[54],"numbers":[58],"satisfies":[59],"unexpected":[61],"recurrence":[62],"n+1":[64],"+":[68],"(1/":[69],").":[72],"\u00a9":[73],"1995":[74],"John":[75],"Wiley":[76],"&amp;":[77],"Sons,":[78],"Inc.":[79]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":7},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":6},{"year":2013,"cited_by_count":6},{"year":2012,"cited_by_count":5}],"updated_date":"2026-06-23T06:36:01.041984","created_date":"2025-10-10T00:00:00"}
