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.
Citation
J. Cervantes-Ojeda. M. Gómez-Fuentes. D. González-Moreno. M. Olsen. "Rainbow Connectivity Using a Rank Genetic Algorithm: Moore Cages with Girth Six." J. Appl. Math. 2019 1 - 7, 2019. https://doi.org/10.1155/2019/4073905