On the List Colouring Problem

  • Authors:

  • Olivier Cogis;Jean-Claude König;Jérôme Palaysi

  • Affiliations:

  • -;-;-

  • Venue:
  • ASIAN '02 Proceedings of the7th Asian Computing Science Conference on Advances in Computing Science: Internet Computing and Modeling, Grid Computing, Peer-to-Peer Computing, and Cluster
  • Year:
  • 2002

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Abstract

To colour a graph G from lists (Lv)v驴V (G) is to assign to each vertex v of G one of the colours from its list Lv so that no two adjacent vertices in G are assigned the same colour. The problem, which arises in contexts where all-optical networks are involved, is known to be NP-complete. We are interested in cases where lists of colours are of the same length and show the NP-completeness of the problem when restricted to bipartite graphs (except for lists of length 2, a well known polynomial problem in general). We then show that given any instance of the list colouring problem restricted to lists having the same length l, a solution exists and can be polynomially computed from any k-colouring of the graph, provided that the overall number of available colours does not exceed k l - 1/k - 1.