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DAM
2010

Minimum sum edge colorings of multicycles

10 years 4 months ago
Minimum sum edge colorings of multicycles
In the minimum sum edge coloring problem, we aim to assign natural numbers to edges of a graph, so that adjacent edges receive different numbers, and the sum of the numbers assigned to the edges is minimum. The chromatic edge strength of a graph is the minimum number of colors required in a minimum sum edge coloring of this graph. We study the case of multicycles, defined as cycles with parallel edges, and give a closed-form expression for the chromatic edge strength of a multicycle, thereby extending a theorem due to Berge. It is shown that the minimum sum can be achieved with a number of colors equal to the chromatic index. We also propose simple algorithms for finding a minimum sum edge coloring of a multicycle. Finally, these results are generalized to a large family of minimum cost coloring problems.
Jean Cardinal, Vlady Ravelomanana, Mario Valencia-
Added 10 Dec 2010
Updated 10 Dec 2010
Type Journal
Year 2010
Where DAM
Authors Jean Cardinal, Vlady Ravelomanana, Mario Valencia-Pabon
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