par Cardinal, Jean 
;Ravelomanana, Vlady V.;Valencia-Pabon, Mario M.
Référence Discrete applied mathematics, 158, 12, page (1216-1223)
Publication Publié, 2009
;Ravelomanana, Vlady V.;Valencia-Pabon, Mario M.Référence Discrete applied mathematics, 158, 12, page (1216-1223)
Publication Publié, 2009
Article révisé par les pairs
| Résumé : | 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. © 2009 Elsevier B.V. All rights reserved. |
