Efficient Algorithms for Parameterized H-colorings

Abstract

We study the fixed parameter tractability of the restrictive H-coloring and the restrictive list H-coloring problems, introduced in [DST01]. The parameter-izations are defined by fixing the number of pre-images of a subset C of the vertices in H through a partial weight assignment (C, K). We define two families of partially weighted graphs: the simple and the plain. For the class of simple partially weighted graphs, we show the fixed parameter tractability of the list (H, C, K)-coloring problem. For the more general class of plain partially weighted graphs, we prove the fixed parameter tractability of the (H, C, K)-coloring problem.

An extended abstract containing some of the results in this paper was presented at the 12th Annual European Symposium on Algorithms (ESA 2004).

The work of the first author was partially supported by the Distinció per a la recerca of the Generalitat de Catalunya 2002. The work of the first and third authors was partially supported by the Spanish CICYT project TIN-2004-0795 (GRAMMARS). The work of the second author was partially supported by the Spanish CICYT project TIN-2005-09918-C02-02 (ASCE).