Journal of Applied Mathematics
- J. Appl. Math.
- Volume 2019 (2019), Article ID 4073905, 7 pages.
Rainbow Connectivity Using a Rank Genetic Algorithm: Moore Cages with Girth Six
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.
J. Appl. Math., Volume 2019 (2019), Article ID 4073905, 7 pages.
Received: 12 September 2018
Accepted: 29 January 2019
First available in Project Euclid: 16 May 2019
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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