Minimum Sum Edge Colorings of Multicycles - Computer Science > Discrete MathematicsReport as inadecuate




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Abstract: In the minimum sum edge coloring problem, we aim to assign natural numbers toedges of a graph, so that adjacent edges receive different numbers, and the sumof the numbers assigned to the edges is minimum. The {\em chromatic edgestrength} of a graph is the minimum number of colors required in a minimum sumedge coloring of this graph. We study the case of multicycles, defined ascycles with parallel edges, and give a closed-form expression for the chromaticedge strength of a multicycle, thereby extending a theorem due to Berge. It isshown that the minimum sum can be achieved with a number of colors equal to thechromatic index. We also propose simple algorithms for finding a minimum sumedge coloring of a multicycle. Finally, these results are generalized to alarge family of minimum cost coloring problems.



Author: Jean Cardinal ULB, Vlady Ravelomanana LIPN, Mario Valencia-Pabon LIPN

Source: https://arxiv.org/







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