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

Abstract EN

A rainbow t-coloring of a t-connected graph G is an edge coloring such that for any two distinct vertices u and v of G there are at least t internally vertex-disjoint rainbow (u,v)-paths.

In this work, we apply a Rank Genetic Algorithm to search for rainbow t-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 rainbow t-colorings with a small number of colors.