{"id":"https://openalex.org/W2013530559","doi":"https://doi.org/10.1016/s0012-365x(01)00117-0","title":"Relations among the fractional chromatic, choice, Hall, and Hall-condition numbers of simple graphs","display_name":"Relations among the fractional chromatic, choice, Hall, and Hall-condition numbers of simple graphs","publication_year":2001,"publication_date":"2001-10-01","ids":{"openalex":"https://openalex.org/W2013530559","doi":"https://doi.org/10.1016/s0012-365x(01)00117-0","mag":"2013530559"},"language":"en","primary_location":{"id":"doi:10.1016/s0012-365x(01)00117-0","is_oa":false,"landing_page_url":"https://doi.org/10.1016/s0012-365x(01)00117-0","pdf_url":null,"source":{"id":"https://openalex.org/S18902827","display_name":"Discrete Mathematics","issn_l":"0012-365X","issn":["0012-365X","1872-681X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"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/A5066820962","display_name":"Amir Daneshgar","orcid":"https://orcid.org/0000-0002-2639-5376"},"institutions":[{"id":"https://openalex.org/I133529467","display_name":"Sharif University of Technology","ror":"https://ror.org/024c2fq17","country_code":"IR","type":"education","lineage":["https://openalex.org/I133529467"]}],"countries":["IR"],"is_corresponding":true,"raw_author_name":"A. Daneshgar","raw_affiliation_strings":["Department of Mathematical Sciences, Sharif University of Technology, P.O. Box 11365\u20139415, Tehran, Iran#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, Sharif University of Technology, P.O. Box 11365\u20139415, Tehran, Iran#TAB#","institution_ids":["https://openalex.org/I133529467"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5111674420","display_name":"A. J. W. Hilton","orcid":null},"institutions":[{"id":"https://openalex.org/I71052956","display_name":"University of Reading","ror":"https://ror.org/05v62cm79","country_code":"GB","type":"education","lineage":["https://openalex.org/I71052956"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"A.J.W. Hilton","raw_affiliation_strings":["Department of Mathematics, The University of Reading, Whiteknights, Reading RG6 2AX, UK"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, The University of Reading, Whiteknights, Reading RG6 2AX, UK","institution_ids":["https://openalex.org/I71052956"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5103004820","display_name":"Paul D. Johnson","orcid":"https://orcid.org/0009-0008-9798-6772"},"institutions":[{"id":"https://openalex.org/I82497590","display_name":"Auburn University","ror":"https://ror.org/02v80fc35","country_code":"US","type":"education","lineage":["https://openalex.org/I82497590"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"P.D. Johnson Jr.","raw_affiliation_strings":["Department of Discrete and Statistical Sciences, 120 Math Annex, Auburn University, AL 36849, USA"],"affiliations":[{"raw_affiliation_string":"Department of Discrete and Statistical Sciences, 120 Math Annex, Auburn University, AL 36849, USA","institution_ids":["https://openalex.org/I82497590"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5066820962"],"corresponding_institution_ids":["https://openalex.org/I133529467"],"apc_list":{"value":3000,"currency":"USD","value_usd":3000},"apc_paid":null,"fwci":1.8542,"has_fulltext":false,"cited_by_count":20,"citation_normalized_percentile":{"value":0.84422148,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"241","issue":"1-3","first_page":"189","last_page":"199"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9973000288009644,"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/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9973000288009644,"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":0.996399998664856,"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"}},{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9962999820709229,"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/mathematics","display_name":"Mathematics","score":0.8677836656570435},{"id":"https://openalex.org/keywords/chromatic-scale","display_name":"Chromatic scale","score":0.686962366104126},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.6685561537742615},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6131863594055176},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.44042885303497314}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8677836656570435},{"id":"https://openalex.org/C196956537","wikidata":"https://www.wikidata.org/wiki/Q202021","display_name":"Chromatic scale","level":2,"score":0.686962366104126},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.6685561537742615},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6131863594055176},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.44042885303497314},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1016/s0012-365x(01)00117-0","is_oa":false,"landing_page_url":"https://doi.org/10.1016/s0012-365x(01)00117-0","pdf_url":null,"source":{"id":"https://openalex.org/S18902827","display_name":"Discrete Mathematics","issn_l":"0012-365X","issn":["0012-365X","1872-681X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete Mathematics","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":8,"referenced_works":["https://openalex.org/W617577063","https://openalex.org/W1980333416","https://openalex.org/W1996343359","https://openalex.org/W2039915592","https://openalex.org/W2059233598","https://openalex.org/W2063292248","https://openalex.org/W2089857193","https://openalex.org/W2327315803"],"related_works":["https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4245490552","https://openalex.org/W4225152035","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W1587224694","https://openalex.org/W2911598644","https://openalex.org/W2142036596"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2014,"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"}