{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,30]],"date-time":"2025-10-30T07:10:42Z","timestamp":1761808242034,"version":"3.37.3"},"reference-count":18,"publisher":"Wiley","license":[{"start":{"date-parts":[[2019,3,3]],"date-time":"2019-03-03T00:00:00Z","timestamp":1551571200000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Universidad Aut\u00f3noma Metropolitana-Cuajimalpa"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2019,3,3]]},"abstract":"<jats:p>A<jats:italic>rainbow<\/jats:italic><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\"><mml:mrow><mml:mi>t<\/mml:mi><\/mml:mrow><\/mml:math><jats:italic>-coloring<\/jats:italic>of a<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M2\"><mml:mrow><mml:mi>t<\/mml:mi><\/mml:mrow><\/mml:math>-connected graph<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M3\"><mml:mrow><mml:mi>G<\/mml:mi><\/mml:mrow><\/mml:math>is an edge coloring such that for any two distinct vertices<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M4\"><mml:mrow><mml:mi>u<\/mml:mi><\/mml:mrow><\/mml:math>and<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M5\"><mml:mrow><mml:mi>v<\/mml:mi><\/mml:mrow><\/mml:math>of<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M6\"><mml:mrow><mml:mi>G<\/mml:mi><\/mml:mrow><\/mml:math>there are at least<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M7\"><mml:mrow><mml:mi>t<\/mml:mi><\/mml:mrow><\/mml:math>internally vertex-disjoint rainbow<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M8\"><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mi>u<\/mml:mi><mml:mo>,<\/mml:mo><mml:mi>v<\/mml:mi><mml:mo stretchy=\"false\">)<\/mml:mo><\/mml:math>-paths. In this work, we apply a Rank Genetic Algorithm to search for rainbow<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M9\"><mml:mrow><mml:mi>t<\/mml:mi><\/mml:mrow><\/mml:math>-colorings of the family of Moore cages with girth six<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M10\"><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mi>t<\/mml:mi><mml:mo>;<\/mml:mo><mml:mn mathvariant=\"normal\">6<\/mml:mn><mml:mo stretchy=\"false\">)<\/mml:mo><\/mml:math>-cages. We found that an upper bound in the number of colors needed to produce a rainbow 4-coloring of a<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M11\"><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mn mathvariant=\"normal\">4<\/mml:mn><mml:mo>;<\/mml:mo><mml:mn mathvariant=\"normal\">6<\/mml:mn><mml:mo stretchy=\"false\">)<\/mml:mo><\/mml:math>-cage is 7, improving the one currently known, which is 13. The computation of the minimum number of colors of a rainbow coloring is known to be NP-Hard and the Rank Genetic Algorithm showed good behavior finding rainbow<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M12\"><mml:mrow><mml:mi>t<\/mml:mi><\/mml:mrow><\/mml:math>-colorings with a small number of colors.<\/jats:p>","DOI":"10.1155\/2019\/4073905","type":"journal-article","created":{"date-parts":[[2019,3,3]],"date-time":"2019-03-03T23:33:38Z","timestamp":1551656018000},"page":"1-7","source":"Crossref","is-referenced-by-count":4,"title":["Rainbow Connectivity Using a Rank Genetic Algorithm: Moore Cages with Girth Six"],"prefix":"10.1155","volume":"2019","author":[{"given":"J.","family":"Cervantes-Ojeda","sequence":"first","affiliation":[{"name":"Universidad Aut\u00f3noma Metropolitana, Cuajimalpa 05348, Mexico"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0033-4476","authenticated-orcid":true,"given":"M.","family":"G\u00f3mez-Fuentes","sequence":"additional","affiliation":[{"name":"Universidad Aut\u00f3noma Metropolitana, Cuajimalpa 05348, Mexico"}]},{"given":"D.","family":"Gonz\u00e1lez-Moreno","sequence":"additional","affiliation":[{"name":"Universidad Aut\u00f3noma Metropolitana, Cuajimalpa 05348, Mexico"}]},{"given":"M.","family":"Olsen","sequence":"additional","affiliation":[{"name":"Universidad Aut\u00f3noma Metropolitana, Cuajimalpa 05348, Mexico"}]}],"member":"311","reference":[{"year":"2013","key":"9"},{"journal-title":"International Computer Games Association","first-page":"124","year":"1989","key":"11"},{"key":"10","doi-asserted-by":"publisher","DOI":"10.1016\/0377-2217(94)00166-9"},{"key":"19","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2013.05.057"},{"key":"3","doi-asserted-by":"publisher","DOI":"10.1109\/TEVC.2008.927707"},{"key":"20","doi-asserted-by":"publisher","DOI":"10.4064\/fm-10-1-96-115"},{"key":"7","doi-asserted-by":"publisher","DOI":"10.1002\/net.20296"},{"issue":"1","key":"6","doi-asserted-by":"crossref","first-page":"85","DOI":"10.21136\/MB.2008.133947","volume":"133","year":"2008","journal-title":"Mathematica Bohemica"},{"journal-title":"Graduating Engineer and Computer Careers","first-page":"24","year":"2007","key":"12"},{"key":"16","doi-asserted-by":"publisher","DOI":"10.1007\/s00373-012-1243-2"},{"year":"2013","series-title":"Springer","key":"17"},{"volume":"ds16","journal-title":"The Electronic Journal of Combinatorics","year":"2013","key":"13"},{"volume":"14","journal-title":"The Electronic Journal of Combinatorics - Dynamic Surveys","year":"2005","key":"21"},{"key":"2","first-page":"191","volume":"20","year":"1973","journal-title":"Journal of the Faculty of Science. 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