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1 MASCOTTE - Algorithms, simulation, combinatorics and optimization for telecommunications CRISAM - Inria Sophia Antipolis - Méditerranée , COMRED - COMmunications, Réseaux, systèmes Embarqués et Distribués 2 LIA - Laboratórios de PesquIsa em ComputAção

Abstract : In this paper, we consider a new edge colouring problem: the proportional edge-colouring. Given a graph $G$ with positive weights associated to its edges, we want to find a colouring which preserves the proportion given by the weights associated to each edge. If such colouring exists, we want to find one using a minimum number of colours. We proved that deciding if a weighted graph admits a proportional colouring is polynomial while determining its proportional chromatic index is NP-hard. In addition, we give a lower bound and an upper bound for this parameter that can be computed in polynomial time. We finally show a class of graphs and a class of weighted graphs for which we can exactly determine the proportional chromatic index.





Autor: Florian Huc - Claudia Linhares Sales - Hervé Rivano -

Fuente: https://hal.archives-ouvertes.fr/



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