{"id":"https://openalex.org/W2057972598","doi":"https://doi.org/10.1007/s00224-012-9410-7","title":"Colorings with few Colors: Counting, Enumeration and Combinatorial Bounds","display_name":"Colorings with few Colors: Counting, Enumeration and Combinatorial Bounds","publication_year":2012,"publication_date":"2012-05-10","ids":{"openalex":"https://openalex.org/W2057972598","doi":"https://doi.org/10.1007/s00224-012-9410-7","mag":"2057972598"},"language":"en","primary_location":{"id":"doi:10.1007/s00224-012-9410-7","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00224-012-9410-7","pdf_url":null,"source":{"id":"https://openalex.org/S4210177266","display_name":"Theory of Computing Systems","issn_l":"1432-4350","issn":["1432-4350","1433-0490"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Theory of Computing Systems","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/A5054371129","display_name":"Jean-Fra\u0146cois Couturier","orcid":null},"institutions":[{"id":"https://openalex.org/I4210116548","display_name":"Laboratoire de Statistique Th\u00e9orique et Appliqu\u00e9e","ror":"https://ror.org/01vnn4t89","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I39804081","https://openalex.org/I4210116548","https://openalex.org/I4210141950"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Jean-Francois Couturier","raw_affiliation_strings":["Laboratoire d\u2019Informatique Th\u00e9orique et Appliqu\u00e9e, Universit\u00e9 Paul Verlaine \u2013 Metz, 57045, Metz Cedex 01, France","Laboratoire d'Informatique Th\u00e9orique et Appliqu\u00e9e"],"affiliations":[{"raw_affiliation_string":"Laboratoire d\u2019Informatique Th\u00e9orique et Appliqu\u00e9e, Universit\u00e9 Paul Verlaine \u2013 Metz, 57045, Metz Cedex 01, France","institution_ids":[]},{"raw_affiliation_string":"Laboratoire d'Informatique Th\u00e9orique et Appliqu\u00e9e","institution_ids":["https://openalex.org/I4210116548"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5051709720","display_name":"Petr A. Golovach","orcid":"https://orcid.org/0000-0002-2619-2990"},"institutions":[{"id":"https://openalex.org/I190082696","display_name":"Durham University","ror":"https://ror.org/01v29qb04","country_code":"GB","type":"education","lineage":["https://openalex.org/I190082696"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Petr A. Golovach","raw_affiliation_strings":["School of Engineering and Computing Sciences, Durham University, South Road, Durham, DH1 3LE, UK","Department of Informatics [Bergen]","School of Engineering and Computing Sciences"],"affiliations":[{"raw_affiliation_string":"School of Engineering and Computing Sciences, Durham University, South Road, Durham, DH1 3LE, UK","institution_ids":["https://openalex.org/I190082696"]},{"raw_affiliation_string":"Department of Informatics [Bergen]","institution_ids":[]},{"raw_affiliation_string":"School of Engineering and Computing Sciences","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5109894460","display_name":"Dieter Kratsch","orcid":null},"institutions":[{"id":"https://openalex.org/I4210116548","display_name":"Laboratoire de Statistique Th\u00e9orique et Appliqu\u00e9e","ror":"https://ror.org/01vnn4t89","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I39804081","https://openalex.org/I4210116548","https://openalex.org/I4210141950"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Dieter Kratsch","raw_affiliation_strings":["Laboratoire d\u2019Informatique Th\u00e9orique et Appliqu\u00e9e, Universit\u00e9 Paul Verlaine \u2013 Metz, 57045, Metz Cedex 01, France","Laboratoire d'Informatique Th\u00e9orique et Appliqu\u00e9e"],"affiliations":[{"raw_affiliation_string":"Laboratoire d\u2019Informatique Th\u00e9orique et Appliqu\u00e9e, Universit\u00e9 Paul Verlaine \u2013 Metz, 57045, Metz Cedex 01, France","institution_ids":[]},{"raw_affiliation_string":"Laboratoire d'Informatique Th\u00e9orique et Appliqu\u00e9e","institution_ids":["https://openalex.org/I4210116548"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5070492372","display_name":"Mathieu Liedloff","orcid":"https://orcid.org/0000-0003-2518-606X"},"institutions":[{"id":"https://openalex.org/I12449238","display_name":"Universit\u00e9 d'Orl\u00e9ans","ror":"https://ror.org/014zrew76","country_code":"FR","type":"education","lineage":["https://openalex.org/I12449238"]},{"id":"https://openalex.org/I4210115196","display_name":"Laboratoire d\u2019Informatique Fondamentale de Marseille","ror":"https://ror.org/022my8t07","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I21491767","https://openalex.org/I4210115196","https://openalex.org/I4210142724","https://openalex.org/I4210159245"]},{"id":"https://openalex.org/I4387153997","display_name":"Laboratoire d'Informatique Fondamentale d'Orl\u00e9ans","ror":"https://ror.org/01nr3td38","country_code":null,"type":"facility","lineage":["https://openalex.org/I12449238","https://openalex.org/I4210143826","https://openalex.org/I4387153997"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Mathieu Liedloff","raw_affiliation_strings":["Laboratoire d\u2019Informatique Fondamentale d\u2019Orl\u00e9ans, Universit\u00e9 d\u2019Orl\u00e9ans, 45067, Orl\u00e9ans Cedex 2, France","Laboratoire d'Informatique Fondamentale d'Orl\u00e9ans"],"affiliations":[{"raw_affiliation_string":"Laboratoire d\u2019Informatique Fondamentale d\u2019Orl\u00e9ans, Universit\u00e9 d\u2019Orl\u00e9ans, 45067, Orl\u00e9ans Cedex 2, France","institution_ids":["https://openalex.org/I12449238"]},{"raw_affiliation_string":"Laboratoire d'Informatique Fondamentale d'Orl\u00e9ans","institution_ids":["https://openalex.org/I4210115196","https://openalex.org/I4387153997"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5089643426","display_name":"A. V. Pyatkin","orcid":"https://orcid.org/0000-0001-5355-411X"},"institutions":[{"id":"https://openalex.org/I190082696","display_name":"Durham University","ror":"https://ror.org/01v29qb04","country_code":"GB","type":"education","lineage":["https://openalex.org/I190082696"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Artem Pyatkin","raw_affiliation_strings":["School of Engineering and Computing Sciences, Durham University, South Road, Durham, DH1 3LE, UK","School of Engineering and Computing Sciences"],"affiliations":[{"raw_affiliation_string":"School of Engineering and Computing Sciences, Durham University, South Road, Durham, DH1 3LE, UK","institution_ids":["https://openalex.org/I190082696"]},{"raw_affiliation_string":"School of Engineering and Computing Sciences","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5054371129"],"corresponding_institution_ids":["https://openalex.org/I4210116548"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":0.6959,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.720364,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"52","issue":"4","first_page":"645","last_page":"667"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9995999932289124,"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":0.9995999932289124,"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/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9988999962806702,"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":0.9735000133514404,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8953160047531128},{"id":"https://openalex.org/keywords/enumeration","display_name":"Enumeration","score":0.8252311944961548},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7415139079093933},{"id":"https://openalex.org/keywords/edge-coloring","display_name":"Edge coloring","score":0.631695032119751},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5158657431602478},{"id":"https://openalex.org/keywords/greedy-coloring","display_name":"Greedy coloring","score":0.5141816139221191},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.500795841217041},{"id":"https://openalex.org/keywords/complete-coloring","display_name":"Complete coloring","score":0.4671838581562042},{"id":"https://openalex.org/keywords/counting-problem","display_name":"Counting problem","score":0.44742682576179504},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.4313521385192871},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.43036895990371704},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.20062986016273499},{"id":"https://openalex.org/keywords/graph-power","display_name":"Graph power","score":0.16832491755485535}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8953160047531128},{"id":"https://openalex.org/C156340839","wikidata":"https://www.wikidata.org/wiki/Q2704791","display_name":"Enumeration","level":2,"score":0.8252311944961548},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7415139079093933},{"id":"https://openalex.org/C123809776","wikidata":"https://www.wikidata.org/wiki/Q1050972","display_name":"Edge coloring","level":5,"score":0.631695032119751},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5158657431602478},{"id":"https://openalex.org/C38767284","wikidata":"https://www.wikidata.org/wiki/Q5601715","display_name":"Greedy coloring","level":5,"score":0.5141816139221191},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.500795841217041},{"id":"https://openalex.org/C21642379","wikidata":"https://www.wikidata.org/wiki/Q3342988","display_name":"Complete coloring","level":5,"score":0.4671838581562042},{"id":"https://openalex.org/C16592021","wikidata":"https://www.wikidata.org/wiki/Q5177154","display_name":"Counting problem","level":2,"score":0.44742682576179504},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.4313521385192871},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.43036895990371704},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.20062986016273499},{"id":"https://openalex.org/C149530733","wikidata":"https://www.wikidata.org/wiki/Q5597091","display_name":"Graph power","level":4,"score":0.16832491755485535},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s00224-012-9410-7","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00224-012-9410-7","pdf_url":null,"source":{"id":"https://openalex.org/S4210177266","display_name":"Theory of Computing Systems","issn_l":"1432-4350","issn":["1432-4350","1433-0490"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Theory of Computing Systems","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-00942919v1","is_oa":false,"landing_page_url":"https://hal.science/hal-00942919","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Theory of Computing Systems, 2013, 52 (4), pp.645-667. ⟨10.1007/s00224-012-9410-7⟩","raw_type":"Journal articles"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1111885211","display_name":null,"funder_award_id":"EP/G043434/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G7542531937","display_name":null,"funder_award_id":"EP/F064551/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":37,"referenced_works":["https://openalex.org/W143512583","https://openalex.org/W1533811829","https://openalex.org/W1579538307","https://openalex.org/W1582963151","https://openalex.org/W1593916827","https://openalex.org/W1598159863","https://openalex.org/W1978463456","https://openalex.org/W2002425091","https://openalex.org/W2009384947","https://openalex.org/W2010629352","https://openalex.org/W2011039300","https://openalex.org/W2013568176","https://openalex.org/W2015963099","https://openalex.org/W2050181703","https://openalex.org/W2068633285","https://openalex.org/W2069200088","https://openalex.org/W2080290639","https://openalex.org/W2080732177","https://openalex.org/W2085870956","https://openalex.org/W2096623634","https://openalex.org/W2102669784","https://openalex.org/W2118902335","https://openalex.org/W2134046427","https://openalex.org/W2146774612","https://openalex.org/W2154399201","https://openalex.org/W2154475159","https://openalex.org/W2159366821","https://openalex.org/W2163938320","https://openalex.org/W2169165595","https://openalex.org/W2170702810","https://openalex.org/W2184661648","https://openalex.org/W2204989461","https://openalex.org/W2561675875","https://openalex.org/W2604810098","https://openalex.org/W4213368513","https://openalex.org/W4285719527","https://openalex.org/W4389615622"],"related_works":["https://openalex.org/W4311345810","https://openalex.org/W1542397451","https://openalex.org/W4291316360","https://openalex.org/W3169197204","https://openalex.org/W2585997002","https://openalex.org/W1994361334","https://openalex.org/W2385428710","https://openalex.org/W2380525562","https://openalex.org/W4229747356","https://openalex.org/W3000828483"],"abstract_inverted_index":null,"counts_by_year":[{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}