{"id":"https://openalex.org/W2093508050","doi":"https://doi.org/10.1007/s00373-013-1298-8","title":"Minimum Number of Palettes in Edge Colorings","display_name":"Minimum Number of Palettes in Edge Colorings","publication_year":2013,"publication_date":"2013-03-19","ids":{"openalex":"https://openalex.org/W2093508050","doi":"https://doi.org/10.1007/s00373-013-1298-8","mag":"2093508050"},"language":"en","primary_location":{"id":"doi:10.1007/s00373-013-1298-8","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00373-013-1298-8","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00373-013-1298-8.pdf","source":{"id":"https://openalex.org/S186126824","display_name":"Graphs and Combinatorics","issn_l":"0911-0119","issn":["0911-0119","1435-5914"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Graphs and Combinatorics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s00373-013-1298-8.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5055656391","display_name":"Mirko Hor\u0148\u00e1k","orcid":"https://orcid.org/0000-0002-3588-8455"},"institutions":[{"id":"https://openalex.org/I204881574","display_name":"University of Pavol Jozef \u0160af\u00e1rik","ror":"https://ror.org/039965637","country_code":"SK","type":"education","lineage":["https://openalex.org/I204881574"]}],"countries":["SK"],"is_corresponding":false,"raw_author_name":"Mirko Hor\u0148\u00e1k","raw_affiliation_strings":["Institute of Mathematics, P.J. \u0160af\u00e1rik University, Jesenn\u00e1 5, 040 01, Ko\u0161ice, Slovakia","Institute of Mathematics, P.J. \u0160af\u00e1rik University, Ko\u0161ice, Slovakia 040 01#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Mathematics, P.J. \u0160af\u00e1rik University, Jesenn\u00e1 5, 040 01, Ko\u0161ice, Slovakia","institution_ids":["https://openalex.org/I204881574"]},{"raw_affiliation_string":"Institute of Mathematics, P.J. \u0160af\u00e1rik University, Ko\u0161ice, Slovakia 040 01#TAB#","institution_ids":["https://openalex.org/I204881574"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5087413349","display_name":"Rafa\u0142 Kalinowski","orcid":"https://orcid.org/0000-0002-3021-7433"},"institutions":[{"id":"https://openalex.org/I686019","display_name":"AGH University of Krakow","ror":"https://ror.org/00bas1c41","country_code":"PL","type":"education","lineage":["https://openalex.org/I686019"]}],"countries":["PL"],"is_corresponding":true,"raw_author_name":"Rafa\u0142 Kalinowski","raw_affiliation_strings":["Department of Discrete Mathematics, Faculty of Applied Mathematics AGH, Al. Mickiewicza 30, 30-059, Krak\u00f3w, Poland","Department of Discrete Mathematics, Faculty of Applied Mathematics AGH, Krak\u00f3w, Poland 30-059#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Discrete Mathematics, Faculty of Applied Mathematics AGH, Al. Mickiewicza 30, 30-059, Krak\u00f3w, Poland","institution_ids":["https://openalex.org/I686019"]},{"raw_affiliation_string":"Department of Discrete Mathematics, Faculty of Applied Mathematics AGH, Krak\u00f3w, Poland 30-059#TAB#","institution_ids":["https://openalex.org/I686019"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5054750597","display_name":"Mariusz Meszka","orcid":"https://orcid.org/0000-0003-0785-9339"},"institutions":[{"id":"https://openalex.org/I686019","display_name":"AGH University of Krakow","ror":"https://ror.org/00bas1c41","country_code":"PL","type":"education","lineage":["https://openalex.org/I686019"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Mariusz Meszka","raw_affiliation_strings":["Department of Discrete Mathematics, Faculty of Applied Mathematics AGH, Al. Mickiewicza 30, 30-059, Krak\u00f3w, Poland","Department of Discrete Mathematics, Faculty of Applied Mathematics AGH, Krak\u00f3w, Poland 30-059#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Discrete Mathematics, Faculty of Applied Mathematics AGH, Al. Mickiewicza 30, 30-059, Krak\u00f3w, Poland","institution_ids":["https://openalex.org/I686019"]},{"raw_affiliation_string":"Department of Discrete Mathematics, Faculty of Applied Mathematics AGH, Krak\u00f3w, Poland 30-059#TAB#","institution_ids":["https://openalex.org/I686019"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5085801031","display_name":"Mariusz Wo\u017aniak","orcid":"https://orcid.org/0000-0003-4769-0056"},"institutions":[{"id":"https://openalex.org/I686019","display_name":"AGH University of Krakow","ror":"https://ror.org/00bas1c41","country_code":"PL","type":"education","lineage":["https://openalex.org/I686019"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Mariusz Wo\u017aniak","raw_affiliation_strings":["Department of Discrete Mathematics, Faculty of Applied Mathematics AGH, Al. Mickiewicza 30, 30-059, Krak\u00f3w, Poland","Department of Discrete Mathematics, Faculty of Applied Mathematics AGH, Krak\u00f3w, Poland 30-059#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Discrete Mathematics, Faculty of Applied Mathematics AGH, Al. Mickiewicza 30, 30-059, Krak\u00f3w, Poland","institution_ids":["https://openalex.org/I686019"]},{"raw_affiliation_string":"Department of Discrete Mathematics, Faculty of Applied Mathematics AGH, Krak\u00f3w, Poland 30-059#TAB#","institution_ids":["https://openalex.org/I686019"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5087413349"],"corresponding_institution_ids":["https://openalex.org/I686019"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":{"value":2290,"currency":"EUR","value_usd":2890},"fwci":0.6634,"has_fulltext":true,"cited_by_count":18,"citation_normalized_percentile":{"value":0.71762034,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"30","issue":"3","first_page":"619","last_page":"626"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11666","display_name":"Color Science and Applications","score":0.8586999773979187,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11666","display_name":"Color Science and Applications","score":0.8586999773979187,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.8442000150680542,"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":0.8336597084999084},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7032701373100281},{"id":"https://openalex.org/keywords/edge-coloring","display_name":"Edge coloring","score":0.6892759799957275},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.6120110154151917},{"id":"https://openalex.org/keywords/fractional-coloring","display_name":"Fractional coloring","score":0.5796200037002563},{"id":"https://openalex.org/keywords/list-coloring","display_name":"List coloring","score":0.5246365666389465},{"id":"https://openalex.org/keywords/complete-coloring","display_name":"Complete coloring","score":0.504972517490387},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4467080235481262},{"id":"https://openalex.org/keywords/graph-coloring","display_name":"Graph coloring","score":0.43816789984703064},{"id":"https://openalex.org/keywords/brooks-theorem","display_name":"Brooks' theorem","score":0.4101761281490326},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.38504651188850403},{"id":"https://openalex.org/keywords/graph-power","display_name":"Graph power","score":0.33890628814697266},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.14603883028030396}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8336597084999084},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7032701373100281},{"id":"https://openalex.org/C123809776","wikidata":"https://www.wikidata.org/wiki/Q1050972","display_name":"Edge coloring","level":5,"score":0.6892759799957275},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.6120110154151917},{"id":"https://openalex.org/C158319403","wikidata":"https://www.wikidata.org/wiki/Q5477527","display_name":"Fractional coloring","level":5,"score":0.5796200037002563},{"id":"https://openalex.org/C199594403","wikidata":"https://www.wikidata.org/wiki/Q1130404","display_name":"List coloring","level":5,"score":0.5246365666389465},{"id":"https://openalex.org/C21642379","wikidata":"https://www.wikidata.org/wiki/Q3342988","display_name":"Complete coloring","level":5,"score":0.504972517490387},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4467080235481262},{"id":"https://openalex.org/C76946457","wikidata":"https://www.wikidata.org/wiki/Q504843","display_name":"Graph coloring","level":3,"score":0.43816789984703064},{"id":"https://openalex.org/C51658606","wikidata":"https://www.wikidata.org/wiki/Q512897","display_name":"Brooks' theorem","level":5,"score":0.4101761281490326},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.38504651188850403},{"id":"https://openalex.org/C149530733","wikidata":"https://www.wikidata.org/wiki/Q5597091","display_name":"Graph power","level":4,"score":0.33890628814697266},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.14603883028030396}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s00373-013-1298-8","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00373-013-1298-8","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00373-013-1298-8.pdf","source":{"id":"https://openalex.org/S186126824","display_name":"Graphs and Combinatorics","issn_l":"0911-0119","issn":["0911-0119","1435-5914"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Graphs and Combinatorics","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1007/s00373-013-1298-8","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00373-013-1298-8","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00373-013-1298-8.pdf","source":{"id":"https://openalex.org/S186126824","display_name":"Graphs and Combinatorics","issn_l":"0911-0119","issn":["0911-0119","1435-5914"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Graphs and Combinatorics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3507724112","display_name":null,"funder_award_id":"APVV-0023-10","funder_id":"https://openalex.org/F4320323251","funder_display_name":"Agent\u00fara na Podporu V\u00fdskumu a V\u00fdvoja"},{"id":"https://openalex.org/G6118725969","display_name":null,"funder_award_id":"0023-10","funder_id":"https://openalex.org/F4320323251","funder_display_name":"Agent\u00fara na Podporu V\u00fdskumu a V\u00fdvoja"},{"id":"https://openalex.org/G7772458387","display_name":null,"funder_award_id":"1/0428/10","funder_id":"https://openalex.org/F4320323251","funder_display_name":"Agent\u00fara na Podporu V\u00fdskumu a V\u00fdvoja"},{"id":"https://openalex.org/G8542723525","display_name":null,"funder_award_id":"1/0428/10","funder_id":"https://openalex.org/F4320323641","funder_display_name":"Vedeck\u00e1 Grantov\u00e1 Agent\u00fara M\u0160VVa\u0160 SR a SAV"}],"funders":[{"id":"https://openalex.org/F4320323251","display_name":"Agent\u00fara na Podporu V\u00fdskumu a V\u00fdvoja","ror":"https://ror.org/037nx0e70"},{"id":"https://openalex.org/F4320323641","display_name":"Vedeck\u00e1 Grantov\u00e1 Agent\u00fara M\u0160VVa\u0160 SR a SAV","ror":"https://ror.org/044gwpv05"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2093508050.pdf","grobid_xml":"https://content.openalex.org/works/W2093508050.grobid-xml"},"referenced_works_count":4,"referenced_works":["https://openalex.org/W2063015103","https://openalex.org/W2084488169","https://openalex.org/W2085672062","https://openalex.org/W4255486464"],"related_works":["https://openalex.org/W4311345810","https://openalex.org/W2585997002","https://openalex.org/W398688634","https://openalex.org/W55620969","https://openalex.org/W2603175250","https://openalex.org/W2387718378","https://openalex.org/W2103957069","https://openalex.org/W2062365033","https://openalex.org/W4239742063","https://openalex.org/W3091797996"],"abstract_inverted_index":{"A":[0],"proper":[1,43],"edge-coloring":[2],"of":[3,12,14,24,37,45],"a":[4,46],"graph":[5],"defines":[6],"at":[7],"each":[8],"vertex":[9],"the":[10,22,25,34],"set":[11,19],"colors":[13],"its":[15],"incident":[16],"edges.":[17],"This":[18],"is":[20],"called":[21],"palette":[23],"vertex.":[26],"In":[27],"this":[28],"paper":[29],"we":[30],"are":[31],"interested":[32],"in":[33],"minimum":[35],"number":[36],"palettes":[38],"taken":[39],"over":[40],"all":[41],"possible":[42],"colorings":[44],"graph.":[47]},"counts_by_year":[{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":2},{"year":2019,"cited_by_count":5},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-06-19T17:40:00.097472","created_date":"2025-10-10T00:00:00"}