Minimum Sum Edge Colorings of Multicycles
| dc.creator | Cardinal, Jean | |
| dc.creator | Ravelomanana, Vlady | |
| dc.creator | Valencia-Pabon, Mario | |
| dc.date | 2007-06-26 | |
| dc.date | 2008-01-22 | |
| dc.date.accessioned | 2026-07-07T08:55:25Z | |
| dc.date.available | 2026-07-07T08:55:25Z | |
| dc.description | 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 {\em 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. | |
| dc.identifier | https://arxiv.org/abs/0706.3848 | |
| dc.identifier | http://arxiv.org/abs/0706.3848 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/146267 | |
| dc.subject | Discrete Mathematics | |
| dc.subject | G.2.2 | |
| dc.title | Minimum Sum Edge Colorings of Multicycles | |
| dc.type | text |