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Rainbow Connectivity Using a Rank Genetic Algorithm: Moore Cages with Girth Six

M. Olsen (), D. González-Moreno (), J. Cervantes-Ojeda () and M. Gómez-Fuentes ()

Journal of Applied Mathematics, 2019, vol. 2019, 1-7

Abstract: A rainbow -coloring of a - connected graph is an edge coloring such that for any two distinct vertices and of there are at least internally vertex-disjoint rainbow - paths. In this work, we apply a Rank Genetic Algorithm to search for rainbow - colorings of the family of Moore cages with girth six - cages. We found that an upper bound in the number of colors needed to produce a rainbow 4-coloring of a - 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 - colorings with a small number of colors.

Date: 2019
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DOI: 10.1155/2019/4073905

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