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


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.


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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.


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

zbMATH: 07132121
MathSciNet: MR3924131
Digital Object Identifier: 10.1155/2019/4073905

Rights: Copyright © 2019 Hindawi


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