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

Author:

Cervantes-Ojeda J.1,Gómez-Fuentes M.1ORCID,González-Moreno D.1,Olsen M.1

Affiliation:

1. Universidad Autónoma Metropolitana, Cuajimalpa 05348, Mexico

Abstract

Arainbowt-coloringof at-connected graphGis an edge coloring such that for any two distinct verticesuandvofGthere are at leasttinternally vertex-disjoint rainbow(u,v)-paths. In this work, we apply a Rank Genetic Algorithm to search for rainbowt-colorings of the family of Moore cages with girth six(t;6)-cages. We found that an upper bound in the number of colors needed to produce a rainbow 4-coloring of a(4;6)-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 rainbowt-colorings with a small number of colors.

Funder

Universidad Autónoma Metropolitana-Cuajimalpa

Publisher

Hindawi Limited

Subject

Applied Mathematics

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