{"id":"https://openalex.org/W2999040677","doi":"https://doi.org/10.37236/1158","title":"The Circular Chromatic Index of Flower Snarks","display_name":"The Circular Chromatic Index of Flower Snarks","publication_year":2006,"publication_date":"2006-11-17","ids":{"openalex":"https://openalex.org/W2999040677","doi":"https://doi.org/10.37236/1158","mag":"2999040677"},"language":"en","primary_location":{"id":"doi:10.37236/1158","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1158","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v13i1n20/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/v13i1n20/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5038997298","display_name":"M. Ghebleh","orcid":"https://orcid.org/0000-0003-2291-0892"},"institutions":[{"id":"https://openalex.org/I130701444","display_name":"Georgia Institute of Technology","ror":"https://ror.org/01zkghx44","country_code":"US","type":"education","lineage":["https://openalex.org/I130701444"]},{"id":"https://openalex.org/I18014758","display_name":"Simon Fraser University","ror":"https://ror.org/0213rcc28","country_code":"CA","type":"education","lineage":["https://openalex.org/I18014758"]},{"id":"https://openalex.org/I21250087","display_name":"Charles University","ror":"https://ror.org/024d6js02","country_code":"CZ","type":"education","lineage":["https://openalex.org/I21250087"]}],"countries":["CA","CZ","US"],"is_corresponding":false,"raw_author_name":"Mohammad Ghebleh","raw_affiliation_strings":["Department of Applied Mathematics and","Institute for Theoretical Computer Science \u2020 Charles University Malostransk\u00e9 n\u00e1m\u011bst\u00ed 25 118 00 Prague, Czech Republic","Department of Mathematics Simon Fraser University 8888 University Drive Burnaby, BC, V5A 1S6, Canada","School of Mathematics Georgia Institute of Technology Atlanta, GA 30332, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics and","institution_ids":[]},{"raw_affiliation_string":"Institute for Theoretical Computer Science \u2020 Charles University Malostransk\u00e9 n\u00e1m\u011bst\u00ed 25 118 00 Prague, Czech Republic","institution_ids":["https://openalex.org/I21250087"]},{"raw_affiliation_string":"Department of Mathematics Simon Fraser University 8888 University Drive Burnaby, BC, V5A 1S6, Canada","institution_ids":["https://openalex.org/I18014758"]},{"raw_affiliation_string":"School of Mathematics Georgia Institute of Technology Atlanta, GA 30332, USA","institution_ids":["https://openalex.org/I130701444"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5027559065","display_name":"Daniel Kr\u00e1l\u034f\u030c","orcid":"https://orcid.org/0000-0001-8680-0890"},"institutions":[{"id":"https://openalex.org/I130701444","display_name":"Georgia Institute of Technology","ror":"https://ror.org/01zkghx44","country_code":"US","type":"education","lineage":["https://openalex.org/I130701444"]},{"id":"https://openalex.org/I18014758","display_name":"Simon Fraser University","ror":"https://ror.org/0213rcc28","country_code":"CA","type":"education","lineage":["https://openalex.org/I18014758"]},{"id":"https://openalex.org/I21250087","display_name":"Charles University","ror":"https://ror.org/024d6js02","country_code":"CZ","type":"education","lineage":["https://openalex.org/I21250087"]}],"countries":["CA","CZ","US"],"is_corresponding":false,"raw_author_name":"Daniel Kr\u00e1l'","raw_affiliation_strings":["Department of Applied Mathematics and","Institute for Theoretical Computer Science \u2020 Charles University Malostransk\u00e9 n\u00e1m\u011bst\u00ed 25 118 00 Prague, Czech Republic","Department of Mathematics Simon Fraser University 8888 University Drive Burnaby, BC, V5A 1S6, Canada","School of Mathematics Georgia Institute of Technology Atlanta, GA 30332, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics and","institution_ids":[]},{"raw_affiliation_string":"Institute for Theoretical Computer Science \u2020 Charles University Malostransk\u00e9 n\u00e1m\u011bst\u00ed 25 118 00 Prague, Czech Republic","institution_ids":["https://openalex.org/I21250087"]},{"raw_affiliation_string":"Department of Mathematics Simon Fraser University 8888 University Drive Burnaby, BC, V5A 1S6, Canada","institution_ids":["https://openalex.org/I18014758"]},{"raw_affiliation_string":"School of Mathematics Georgia Institute of Technology Atlanta, GA 30332, USA","institution_ids":["https://openalex.org/I130701444"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5042313945","display_name":"Serguei Norine","orcid":null},"institutions":[{"id":"https://openalex.org/I130701444","display_name":"Georgia Institute of Technology","ror":"https://ror.org/01zkghx44","country_code":"US","type":"education","lineage":["https://openalex.org/I130701444"]},{"id":"https://openalex.org/I18014758","display_name":"Simon Fraser University","ror":"https://ror.org/0213rcc28","country_code":"CA","type":"education","lineage":["https://openalex.org/I18014758"]},{"id":"https://openalex.org/I21250087","display_name":"Charles University","ror":"https://ror.org/024d6js02","country_code":"CZ","type":"education","lineage":["https://openalex.org/I21250087"]}],"countries":["CA","CZ","US"],"is_corresponding":false,"raw_author_name":"Serguei Norine","raw_affiliation_strings":["Department of Mathematics Simon Fraser University 8888 University Drive Burnaby, BC, V5A 1S6, Canada","Department of Applied Mathematics and","School of Mathematics Georgia Institute of Technology Atlanta, GA 30332, USA","Institute for Theoretical Computer Science \u2020 Charles University Malostransk\u00e9 n\u00e1m\u011bst\u00ed 25 118 00 Prague, Czech Republic"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics Simon Fraser University 8888 University Drive Burnaby, BC, V5A 1S6, Canada","institution_ids":["https://openalex.org/I18014758"]},{"raw_affiliation_string":"Department of Applied Mathematics and","institution_ids":[]},{"raw_affiliation_string":"School of Mathematics Georgia Institute of Technology Atlanta, GA 30332, USA","institution_ids":["https://openalex.org/I130701444"]},{"raw_affiliation_string":"Institute for Theoretical Computer Science \u2020 Charles University Malostransk\u00e9 n\u00e1m\u011bst\u00ed 25 118 00 Prague, Czech Republic","institution_ids":["https://openalex.org/I21250087"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101892672","display_name":"Robin Thomas","orcid":"https://orcid.org/0000-0002-9318-1458"},"institutions":[{"id":"https://openalex.org/I130701444","display_name":"Georgia Institute of Technology","ror":"https://ror.org/01zkghx44","country_code":"US","type":"education","lineage":["https://openalex.org/I130701444"]},{"id":"https://openalex.org/I18014758","display_name":"Simon Fraser University","ror":"https://ror.org/0213rcc28","country_code":"CA","type":"education","lineage":["https://openalex.org/I18014758"]},{"id":"https://openalex.org/I21250087","display_name":"Charles University","ror":"https://ror.org/024d6js02","country_code":"CZ","type":"education","lineage":["https://openalex.org/I21250087"]}],"countries":["CA","CZ","US"],"is_corresponding":false,"raw_author_name":"Robin Thomas","raw_affiliation_strings":["Department of Mathematics Simon Fraser University 8888 University Drive Burnaby, BC, V5A 1S6, Canada","School of Mathematics Georgia Institute of Technology Atlanta, GA 30332, USA","Department of Applied Mathematics and","Institute for Theoretical Computer Science \u2020 Charles University Malostransk\u00e9 n\u00e1m\u011bst\u00ed 25 118 00 Prague, Czech Republic"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics Simon Fraser University 8888 University Drive Burnaby, BC, V5A 1S6, Canada","institution_ids":["https://openalex.org/I18014758"]},{"raw_affiliation_string":"School of Mathematics Georgia Institute of Technology Atlanta, GA 30332, USA","institution_ids":["https://openalex.org/I130701444"]},{"raw_affiliation_string":"Department of Applied Mathematics and","institution_ids":[]},{"raw_affiliation_string":"Institute for Theoretical Computer Science \u2020 Charles University Malostransk\u00e9 n\u00e1m\u011bst\u00ed 25 118 00 Prague, Czech Republic","institution_ids":["https://openalex.org/I21250087"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.6619,"has_fulltext":true,"cited_by_count":16,"citation_normalized_percentile":{"value":0.90388079,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"13","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9991000294685364,"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":0.9991000294685364,"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":0.9962000250816345,"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/T11797","display_name":"graph theory and CDMA systems","score":0.994700014591217,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8699432611465454},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8601534962654114},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.6460871696472168},{"id":"https://openalex.org/keywords/chromatic-scale","display_name":"Chromatic scale","score":0.6151564717292786},{"id":"https://openalex.org/keywords/edge-coloring","display_name":"Edge coloring","score":0.5096666812896729},{"id":"https://openalex.org/keywords/index","display_name":"Index (typography)","score":0.4978494644165039},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.28415215015411377}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8699432611465454},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8601534962654114},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.6460871696472168},{"id":"https://openalex.org/C196956537","wikidata":"https://www.wikidata.org/wiki/Q202021","display_name":"Chromatic scale","level":2,"score":0.6151564717292786},{"id":"https://openalex.org/C123809776","wikidata":"https://www.wikidata.org/wiki/Q1050972","display_name":"Edge coloring","level":5,"score":0.5096666812896729},{"id":"https://openalex.org/C2777382242","wikidata":"https://www.wikidata.org/wiki/Q6017816","display_name":"Index (typography)","level":2,"score":0.4978494644165039},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.28415215015411377},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.0},{"id":"https://openalex.org/C149530733","wikidata":"https://www.wikidata.org/wiki/Q5597091","display_name":"Graph power","level":4,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C136764020","wikidata":"https://www.wikidata.org/wiki/Q466","display_name":"World Wide Web","level":1,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.37236/1158","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1158","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v13i1n20/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:10.1.1.378.7801","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.378.7801","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"https://web.math.princeton.edu/~snorin/papers/flower.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.71.5121","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.71.5121","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://kam.mff.cuni.cz/~kamserie/serie/clanky/2005/s731.ps","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.91.7519","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.91.7519","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.emis.de/journals/EJC/Volume_13/PDF/v13i1n20.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.92.7562","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.92.7562","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://iti.mff.cuni.cz/series/files/iti252.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.37236/1158","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1158","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v13i1n20/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/G1758806113","display_name":"Characterization and Recognition of Perfect Graphs","funder_award_id":"0200595","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8161222369","display_name":"FRG: Collaborative Research: The Four-Color Theorem and Beyond","funder_award_id":"0354742","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320324094","display_name":"Technische Universit\u00e4t Berlin","ror":"https://ror.org/03v4gjf40"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2999040677.pdf","grobid_xml":"https://content.openalex.org/works/W2999040677.grobid-xml"},"referenced_works_count":13,"referenced_works":["https://openalex.org/W345637930","https://openalex.org/W1526979981","https://openalex.org/W1563416066","https://openalex.org/W2013273488","https://openalex.org/W2022795828","https://openalex.org/W2047918966","https://openalex.org/W2073039945","https://openalex.org/W2097200419","https://openalex.org/W2130738665","https://openalex.org/W2332265223","https://openalex.org/W2476848496","https://openalex.org/W2951550992","https://openalex.org/W4234132957"],"related_works":["https://openalex.org/W4387838689","https://openalex.org/W1758674513","https://openalex.org/W3191650367","https://openalex.org/W1978273318","https://openalex.org/W2573526532","https://openalex.org/W1986620181","https://openalex.org/W74836192","https://openalex.org/W2536579569","https://openalex.org/W3215188102","https://openalex.org/W2617791081"],"abstract_inverted_index":{"We":[0],"determine":[1],"the":[2,25],"circular":[3],"chromatic":[4],"index":[5],"of":[6],"flower":[7,26],"snarks,":[8],"by":[9],"showing":[10],"that":[11],"$\\chi'_c(F_{3})=7/2$,":[12],"$\\chi'_c(F_{5})=17/5$":[13],"and":[14],"$\\chi'_c(F_{k})=10/3$":[15],"for":[16],"every":[17],"odd":[18],"integer":[19],"$k\\ge":[20],"7$,":[21],"where":[22],"$F_k$":[23],"denotes":[24],"snark":[27],"on":[28],"$4k$":[29],"vertices.":[30]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
