{"id":"https://openalex.org/W4390576738","doi":"https://doi.org/10.1051/ro/2024005","title":"On the oriented coloring of the disjoint union of graphs","display_name":"On the oriented coloring of the disjoint union of graphs","publication_year":2024,"publication_date":"2024-01-01","ids":{"openalex":"https://openalex.org/W4390576738","doi":"https://doi.org/10.1051/ro/2024005"},"language":"en","primary_location":{"id":"doi:10.1051/ro/2024005","is_oa":true,"landing_page_url":"https://doi.org/10.1051/ro/2024005","pdf_url":null,"source":{"id":"https://openalex.org/S20631277","display_name":"RAIRO - Operations Research","issn_l":"0399-0559","issn":["0399-0559","1290-3868","2804-7303"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319748","host_organization_name":"EDP Sciences","host_organization_lineage":["https://openalex.org/P4310319748","https://openalex.org/P4310319982"],"host_organization_lineage_names":["EDP Sciences","Science Press"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"RAIRO - Operations Research","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://doi.org/10.1051/ro/2024005","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5023472150","display_name":"Erika M. M. Coelho","orcid":"https://orcid.org/0000-0002-3234-5789"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Erika Morais Martins Coelho","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5085073374","display_name":"Hebert Coelho da Silva","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Hebert Coelho da Silva","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5102849069","display_name":"Lu\u00e9rbio Faria","orcid":"https://orcid.org/0000-0003-0000-6990"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Luerbio Faria","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5072594543","display_name":"Mateus de Paula Ferreira","orcid":"https://orcid.org/0000-0002-5585-5423"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Mateus de Paula Ferreira","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0002-5585-5423","affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5108218887","display_name":"Sylvain Gravier","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Sylvain Gravier","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5064303324","display_name":"Sulamita Klein","orcid":"https://orcid.org/0000-0003-1524-1264"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Sulamita Klein","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":0,"currency":"USD","value_usd":0},"apc_paid":null,"fwci":0.183,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.41636805,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":94},"biblio":{"volume":"58","issue":"1","first_page":"579","last_page":"590"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T13991","display_name":"Nuclear Receptors and Signaling","score":0.7857000231742859,"subfield":{"id":"https://openalex.org/subfields/2804","display_name":"Cellular and Molecular Neuroscience"},"field":{"id":"https://openalex.org/fields/28","display_name":"Neuroscience"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},"topics":[{"id":"https://openalex.org/T13991","display_name":"Nuclear Receptors and Signaling","score":0.7857000231742859,"subfield":{"id":"https://openalex.org/subfields/2804","display_name":"Cellular and Molecular Neuroscience"},"field":{"id":"https://openalex.org/fields/28","display_name":"Neuroscience"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6684754490852356},{"id":"https://openalex.org/keywords/disjoint-sets","display_name":"Disjoint sets","score":0.47466471791267395},{"id":"https://openalex.org/keywords/kadomtsev\u2013petviashvili-equation","display_name":"Kadomtsev\u2013Petviashvili equation","score":0.4606257975101471},{"id":"https://openalex.org/keywords/chromatic-scale","display_name":"Chromatic scale","score":0.45622190833091736},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3768090009689331},{"id":"https://openalex.org/keywords/characteristic-equation","display_name":"Characteristic equation","score":0.37532249093055725},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.27668213844299316},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2578006386756897},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.25602951645851135}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6684754490852356},{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.47466471791267395},{"id":"https://openalex.org/C159785203","wikidata":"https://www.wikidata.org/wiki/Q6345653","display_name":"Kadomtsev\u2013Petviashvili equation","level":4,"score":0.4606257975101471},{"id":"https://openalex.org/C196956537","wikidata":"https://www.wikidata.org/wiki/Q202021","display_name":"Chromatic scale","level":2,"score":0.45622190833091736},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3768090009689331},{"id":"https://openalex.org/C53744967","wikidata":"https://www.wikidata.org/wiki/Q1062971","display_name":"Characteristic equation","level":3,"score":0.37532249093055725},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.27668213844299316},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2578006386756897},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.25602951645851135}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1051/ro/2024005","is_oa":true,"landing_page_url":"https://doi.org/10.1051/ro/2024005","pdf_url":null,"source":{"id":"https://openalex.org/S20631277","display_name":"RAIRO - Operations Research","issn_l":"0399-0559","issn":["0399-0559","1290-3868","2804-7303"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319748","host_organization_name":"EDP Sciences","host_organization_lineage":["https://openalex.org/P4310319748","https://openalex.org/P4310319982"],"host_organization_lineage_names":["EDP Sciences","Science Press"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"RAIRO - Operations Research","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1051/ro/2024005","is_oa":true,"landing_page_url":"https://doi.org/10.1051/ro/2024005","pdf_url":null,"source":{"id":"https://openalex.org/S20631277","display_name":"RAIRO - Operations Research","issn_l":"0399-0559","issn":["0399-0559","1290-3868","2804-7303"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319748","host_organization_name":"EDP Sciences","host_organization_lineage":["https://openalex.org/P4310319748","https://openalex.org/P4310319982"],"host_organization_lineage_names":["EDP Sciences","Science Press"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"RAIRO - Operations Research","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/15","display_name":"Life in Land","score":0.5099999904632568}],"awards":[],"funders":[{"id":"https://openalex.org/F4320321091","display_name":"Coordena\u00e7\u00e3o de Aperfei\u00e7oamento de Pessoal de N\u00edvel Superior","ror":"https://ror.org/00x0ma614"},{"id":"https://openalex.org/F4320322025","display_name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico","ror":"https://ror.org/03swz6y49"},{"id":"https://openalex.org/F4320322749","display_name":"Funda\u00e7\u00e3o Carlos Chagas Filho de Amparo \u00e0 Pesquisa do Estado do Rio de Janeiro","ror":"https://ror.org/03kk0s825"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W1963946273","https://openalex.org/W1965982884","https://openalex.org/W1970463374","https://openalex.org/W1973322735","https://openalex.org/W2002737430","https://openalex.org/W2012113004","https://openalex.org/W2016910331","https://openalex.org/W2046662685","https://openalex.org/W2047915396","https://openalex.org/W2055334092","https://openalex.org/W2055579046","https://openalex.org/W2101212885","https://openalex.org/W2140765647","https://openalex.org/W2165426231","https://openalex.org/W2173582843","https://openalex.org/W2313696863","https://openalex.org/W2508099963","https://openalex.org/W3009788456","https://openalex.org/W3173252628","https://openalex.org/W4231773516"],"related_works":["https://openalex.org/W1971174658","https://openalex.org/W2099195351","https://openalex.org/W4256429076","https://openalex.org/W2012063272","https://openalex.org/W2348092930","https://openalex.org/W2062850566","https://openalex.org/W1553466895","https://openalex.org/W2912783475","https://openalex.org/W1982103020","https://openalex.org/W2385871421"],"abstract_inverted_index":{"LetG\u20d7":[0],"=":[1],"(V,":[2],"A)":[3],"be":[4],"an":[5,50],"oriented":[6,98,104],"graph":[7,10,135,143],"andGthe":[8],"underlying":[9],"ofG\u20d7.":[11],"Anorientedk-coloringofG\u20d7":[12],"is":[13,21,52,116],"a":[14,37,117,145],"partition":[15],"ofVintokcolor":[16],"classes,":[17],"such":[18,121],"that":[19,110],"there":[20,115],"no":[22],"pair":[23,38],"of":[24,39,60,74,77,101,129,132,140],"adjacent":[25],"vertices":[26],"belonging":[27],"to":[28],"the":[29,34,43,61,64,75,83,97,130],"same":[30,44],"class":[31],"and":[32,106,139],"all":[33,68],"arcs":[35],"between":[36],"color":[40],"classes":[41],"have":[42],"orientation.":[45],"The":[46],"smallestksuch":[47],"thatG\u20d7":[48],"admits":[49],"orientedk-coloring":[51],"theoriented":[53],"chromatic":[54,58,72,99],"number\u03c7o(G\u20d7)":[55],"=kofG\u20d7.":[56],"Theoriented":[57],"number\u03c7o(G)":[59],"undirected":[62],"graphGis":[63],"maximum":[65],"of\u03c7o(G\u20d7)":[66],"for":[67,96],"orientationsG\u20d7":[69],"ofG.":[70],"Oriented":[71],"number":[73,100],"product":[76],"two":[78,103,112],"graphsG1,G2was":[79],"widely":[80],"studied,":[81],"but":[82],"disjoint":[84],"unionG1\u222aG2has":[85],"not":[86],"yet":[87],"been":[88],"considered.":[89],"In":[90],"this":[91],"article":[92],"we":[93,107,125],"proved":[94,109],"bounds":[95],"any":[102],"graphs":[105],"also":[108],"given":[111],"complete":[113,134,142],"graphsKnandKmwithn\u2265m,":[114],"real":[118],"number\u03b1\u2208(1,":[119],"3)":[120],"that\u03c7o(Kn\u222aKm)":[122],"=n+m\u2212\u03b1log2(m).":[123],"Additionally,":[124],"established":[126],"exact":[127],"values":[128],"union":[131],"one":[133,137,141],"with":[136,144],"cycle":[138],"forest.":[146]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2026-08-28T12:50:07.497085","created_date":"2025-10-10T00:00:00"}
