{"id":"https://openalex.org/W1995420943","doi":"https://doi.org/10.1002/(sici)1097-0118(199908)31:4<267::aid-jgt1>3.0.co;2-d","title":"The edge chromatic number of a directed/mixed multigraph","display_name":"The edge chromatic number of a directed/mixed multigraph","publication_year":1999,"publication_date":"1999-08-01","ids":{"openalex":"https://openalex.org/W1995420943","doi":"https://doi.org/10.1002/(sici)1097-0118(199908)31:4<267::aid-jgt1>3.0.co;2-d","mag":"1995420943"},"language":"en","primary_location":{"id":"doi:10.1002/(sici)1097-0118(199908)31:4<267::aid-jgt1>3.0.co;2-d","is_oa":false,"landing_page_url":"https://doi.org/10.1002/(sici)1097-0118(199908)31:4<267::aid-jgt1>3.0.co;2-d","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/A5062718264","display_name":"Leonid S. Mel\u2019nikov","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Leonid S. Mel'nikov","raw_affiliation_strings":["Both authors carried out this work during their visit to Odensse University in March, 1995","Institute of Mathematics, Siberian Branch of RAS, Novosibirsk 630090, Russia","Institute of Mathematics, Siberian Branch of RAS, Novosibirsk 630090, Russia#TAB#"],"affiliations":[{"raw_affiliation_string":"Both authors carried out this work during their visit to Odensse University in March, 1995","institution_ids":[]},{"raw_affiliation_string":"Institute of Mathematics, Siberian Branch of RAS, Novosibirsk 630090, Russia","institution_ids":[]},{"raw_affiliation_string":"Institute of Mathematics, Siberian Branch of RAS, Novosibirsk 630090, Russia#TAB#","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5044571803","display_name":"V. G. Vizing","orcid":null},"institutions":[{"id":"https://openalex.org/I227365583","display_name":"Odesa National University of Technology","ror":"https://ror.org/05g6n4k07","country_code":"UA","type":"education","lineage":["https://openalex.org/I227365583"]}],"countries":["UA"],"is_corresponding":false,"raw_author_name":"Vadim G. Vizing","raw_affiliation_strings":["Both authors carried out this work during their visit to Odensse University in March, 1995","Department of Applied Mathematics, Odessa's State Food Technology Academy, Kanatnaja str. 112, Odessa 270039, Ukraine","Department of Applied Mathematics, Odessa's State Food Technology Academy, Kanatnaja str. 112, Odessa 270039, Ukraine#TAB#"],"affiliations":[{"raw_affiliation_string":"Both authors carried out this work during their visit to Odensse University in March, 1995","institution_ids":[]},{"raw_affiliation_string":"Department of Applied Mathematics, Odessa's State Food Technology Academy, Kanatnaja str. 112, Odessa 270039, Ukraine","institution_ids":["https://openalex.org/I227365583"]},{"raw_affiliation_string":"Department of Applied Mathematics, Odessa's State Food Technology Academy, Kanatnaja str. 112, Odessa 270039, Ukraine#TAB#","institution_ids":["https://openalex.org/I227365583"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5062718264"],"corresponding_institution_ids":[],"apc_list":{"value":3760,"currency":"USD","value_usd":3760},"apc_paid":null,"fwci":0.9416,"has_fulltext":false,"cited_by_count":23,"citation_normalized_percentile":{"value":0.73331556,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"31","issue":"4","first_page":"267","last_page":"273"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9970999956130981,"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":0.9970999956130981,"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":0.9958999752998352,"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":0.9887999892234802,"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/multigraph","display_name":"Multigraph","score":0.9600018262863159},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8136801719665527},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.709134578704834},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.6276947259902954},{"id":"https://openalex.org/keywords/edge-coloring","display_name":"Edge coloring","score":0.6004441976547241},{"id":"https://openalex.org/keywords/chromatic-scale","display_name":"Chromatic scale","score":0.5955288410186768},{"id":"https://openalex.org/keywords/undirected-graph","display_name":"Undirected graph","score":0.5224351286888123},{"id":"https://openalex.org/keywords/directed-graph","display_name":"Directed graph","score":0.48209360241889954},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4777242839336395},{"id":"https://openalex.org/keywords/enhanced-data-rates-for-gsm-evolution","display_name":"Enhanced Data Rates for GSM Evolution","score":0.4766198694705963},{"id":"https://openalex.org/keywords/fractional-coloring","display_name":"Fractional coloring","score":0.4637376070022583},{"id":"https://openalex.org/keywords/greedy-coloring","display_name":"Greedy coloring","score":0.4416781961917877},{"id":"https://openalex.org/keywords/graph-coloring","display_name":"Graph coloring","score":0.424530565738678},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1757851243019104},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.1195192039012909},{"id":"https://openalex.org/keywords/graph-power","display_name":"Graph power","score":0.07172852754592896},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.05434712767601013}],"concepts":[{"id":"https://openalex.org/C17758045","wikidata":"https://www.wikidata.org/wiki/Q2642629","display_name":"Multigraph","level":3,"score":0.9600018262863159},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8136801719665527},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.709134578704834},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.6276947259902954},{"id":"https://openalex.org/C123809776","wikidata":"https://www.wikidata.org/wiki/Q1050972","display_name":"Edge coloring","level":5,"score":0.6004441976547241},{"id":"https://openalex.org/C196956537","wikidata":"https://www.wikidata.org/wiki/Q202021","display_name":"Chromatic scale","level":2,"score":0.5955288410186768},{"id":"https://openalex.org/C3018234147","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Undirected graph","level":3,"score":0.5224351286888123},{"id":"https://openalex.org/C146380142","wikidata":"https://www.wikidata.org/wiki/Q1137726","display_name":"Directed graph","level":2,"score":0.48209360241889954},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4777242839336395},{"id":"https://openalex.org/C162307627","wikidata":"https://www.wikidata.org/wiki/Q204833","display_name":"Enhanced Data Rates for GSM Evolution","level":2,"score":0.4766198694705963},{"id":"https://openalex.org/C158319403","wikidata":"https://www.wikidata.org/wiki/Q5477527","display_name":"Fractional coloring","level":5,"score":0.4637376070022583},{"id":"https://openalex.org/C38767284","wikidata":"https://www.wikidata.org/wiki/Q5601715","display_name":"Greedy coloring","level":5,"score":0.4416781961917877},{"id":"https://openalex.org/C76946457","wikidata":"https://www.wikidata.org/wiki/Q504843","display_name":"Graph coloring","level":3,"score":0.424530565738678},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1757851243019104},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.1195192039012909},{"id":"https://openalex.org/C149530733","wikidata":"https://www.wikidata.org/wiki/Q5597091","display_name":"Graph power","level":4,"score":0.07172852754592896},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.05434712767601013}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1002/(sici)1097-0118(199908)31:4<267::aid-jgt1>3.0.co;2-d","is_oa":false,"landing_page_url":"https://doi.org/10.1002/(sici)1097-0118(199908)31:4<267::aid-jgt1>3.0.co;2-d","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"},{"id":"doi:10.1002/(sici)1097-0118(199908)31:4<267::aid-jgt1>3.3.co;2-4","is_oa":false,"landing_page_url":"https://doi.org/10.1002/(sici)1097-0118(199908)31:4<267::aid-jgt1>3.3.co;2-4","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"},{"id":"mag:1995420943","is_oa":false,"landing_page_url":"https://dblp.uni-trier.de/db/journals/jgt/jgt31.html#Rautenbach99","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":null,"is_accepted":false,"is_published":null,"raw_source_name":"Journal of Graph Theory","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":10,"referenced_works":["https://openalex.org/W345637930","https://openalex.org/W1484040084","https://openalex.org/W1486880591","https://openalex.org/W1997657048","https://openalex.org/W2048118184","https://openalex.org/W2053050060","https://openalex.org/W2067603958","https://openalex.org/W2069267595","https://openalex.org/W2112825968","https://openalex.org/W2330003519"],"related_works":["https://openalex.org/W2078629835","https://openalex.org/W2007901221","https://openalex.org/W1485012372","https://openalex.org/W2938065645","https://openalex.org/W2144267444","https://openalex.org/W2350116256","https://openalex.org/W2607340541","https://openalex.org/W2066081866","https://openalex.org/W2215830000","https://openalex.org/W1994012687","https://openalex.org/W2377259416","https://openalex.org/W2603175250","https://openalex.org/W2915216917","https://openalex.org/W2155028150","https://openalex.org/W1964571783","https://openalex.org/W2951268459","https://openalex.org/W2951682971","https://openalex.org/W2050281560","https://openalex.org/W2158850746","https://openalex.org/W2471576094"],"abstract_inverted_index":{"We":[0,20],"consider":[1],"colorings":[2,77],"of":[3,9,18,39,43,52,72,101],"the":[4,37,40,50,53,60,69,81],"directed":[5,30,45,87],"and":[6,28],"undirected":[7,23],"edges":[8],"a":[10,44,91,98],"mixed":[11],"multigraph":[12],"G":[13,84,96],"by":[14],"an":[15],"ordered":[16],"set":[17],"colors.":[19,102],"color":[21,27,38,51],"each":[22,29],"edge":[24,31,46],"in":[25,32],"one":[26],"two":[33],"colors,":[34],"such":[35,76],"that":[36],"first":[41],"half":[42],"is":[47,78,106],"smaller":[48],"than":[49],"second":[54],"half.":[55],"The":[56],"colors":[57,73],"used":[58],"at":[59],"same":[61],"vertex":[62],"are":[63],"all":[64],"different.":[65],"A":[66],"bound":[67],"for":[68,75,94],"minimum":[70,99],"number":[71,100],"needed":[74],"obtained.":[79],"In":[80],"case":[82],"where":[83],"has":[85],"only":[86],"edges,":[88],"we":[89],"provide":[90],"polynomal":[92],"algorithm":[93],"coloring":[95],"with":[97],"An":[103],"unsolved":[104],"problem":[105],"formulated.":[107],"\u00a9":[108],"1999":[109,120],"John":[110],"Wiley":[111],"&":[112],"Sons,":[113],"Inc.":[114],"J":[115],"Graph":[116],"Theory":[117],"31:":[118],"267\u2013273,":[119]},"counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2016-06-24T00:00:00"}
