Fixed Parameter Algorithms for Counting and Deciding Bounded Restrictive List H-Colorings

Abstract

We study the fixed parameter tractability of the parameterized counting and decision version of the restrictive H-coloring problem. These problems are defined by fixing the number of preimages of a subset C of the vertices in H through a partial weight assignment (H,C,K). We consider two families of partial weight assignment the simple and the plain. For simple partial weight assignments we show an FPT algorithm for counting list (H,C,K)-colorings and faster algorithms for its decision version. For the more general class of plain partial weight assignment we give an FPT algorithm for the (H,C,K)-coloring decision problem. We introduce the concept of compactor and an algorithmic technique, compactor enumeration, that allow us to design the FPT algorithms for the counting version (and probably export the technique to other problems).

Partially supported by the EU within FP6 under contract 001907 (DELIS). The first author was further supported by the Distinció per a la Recerca of the Generalitat de Catalunya. The second and third authors were further supported by the Spanish CICYT project TIC-2002-04498-C05-03.