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

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

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.

Suggested Citation

  • J. Cervantes-Ojeda & M. Gómez-Fuentes & D. González-Moreno & M. Olsen, 2019. "Rainbow Connectivity Using a Rank Genetic Algorithm: Moore Cages with Girth Six," Journal of Applied Mathematics, John Wiley & Sons, vol. 2019(1).
    • Handle: RePEc:wly:jnljam:v:2019:y:2019:i:1:n:4073905
    DOI: 10.1155/2019/4073905
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