Journal of Applied Mathematics

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

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

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Abstract

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.

Article information

Source
J. Appl. Math., Volume 2019 (2019), Article ID 4073905, 7 pages.

Dates
Received: 12 September 2018
Accepted: 29 January 2019
First available in Project Euclid: 16 May 2019

Permanent link to this document
https://projecteuclid.org/euclid.jam/1557972261

Digital Object Identifier
doi:10.1155/2019/4073905

Mathematical Reviews number (MathSciNet)
MR3924131

Citation

Cervantes-Ojeda, J.; Gómez-Fuentes, M.; González-Moreno, D.; Olsen, M. Rainbow Connectivity Using a Rank Genetic Algorithm: Moore Cages with Girth Six. J. Appl. Math. 2019 (2019), Article ID 4073905, 7 pages. doi:10.1155/2019/4073905. https://projecteuclid.org/euclid.jam/1557972261


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