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- W2920565532 abstract "A rainbow <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M1><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:math> -coloring of a<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M2><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:math>-connected graph<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M3><mml:mrow><mml:mi>G</mml:mi></mml:mrow></mml:math>is an edge coloring such that for any two distinct vertices<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M4><mml:mrow><mml:mi>u</mml:mi></mml:mrow></mml:math>and<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M5><mml:mrow><mml:mi>v</mml:mi></mml:mrow></mml:math>of<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M6><mml:mrow><mml:mi>G</mml:mi></mml:mrow></mml:math>there are at least<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M7><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:math>internally vertex-disjoint rainbow<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M8><mml:mo stretchy=false>(</mml:mo><mml:mi>u</mml:mi><mml:mo>,</mml:mo><mml:mi>v</mml:mi><mml:mo stretchy=false>)</mml:mo></mml:math>-paths. In this work, we apply a Rank Genetic Algorithm to search for rainbow<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M9><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:math>-colorings of the family of Moore cages with girth six<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M10><mml:mo stretchy=false>(</mml:mo><mml:mi>t</mml:mi><mml:mo>;</mml:mo><mml:mn mathvariant=normal>6</mml:mn><mml:mo stretchy=false>)</mml:mo></mml:math>-cages. We found that an upper bound in the number of colors needed to produce a rainbow 4-coloring of a<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M11><mml:mo stretchy=false>(</mml:mo><mml:mn mathvariant=normal>4</mml:mn><mml:mo>;</mml:mo><mml:mn mathvariant=normal>6</mml:mn><mml:mo stretchy=false>)</mml:mo></mml:math>-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<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M12><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:math>-colorings with a small number of colors." @default.
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- W2920565532 date "2019-03-03" @default.
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- W2920565532 title "Rainbow Connectivity Using a Rank Genetic Algorithm: Moore Cages with Girth Six" @default.
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- W2920565532 doi "https://doi.org/10.1155/2019/4073905" @default.
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