Improved Exact Algorithms for Counting 3- and 4-Colorings

Abstract. We introduce a generic algorithmic technique and apply it on decision and counting versions of graph coloring. Our approach is based on the following idea: either a graph has nice (from the algorithmic point of view) properties which allow a simple recursive procedure to find the solution fast, or the pathwidth of the graph is small, which in turn can be used to find the solution by dynamic programming. By making use of this technique we obtain the fastest known exact algorithms

• Type: Conference
• Year: 2007
• Where: COCOON
• Authors: Fedor V. Fomin, Serge Gaspers, Saket Saurabh
• Keywords: COCOON 2007, Combinatorics, Generic Algorithmic Technique, Graph Coloring, Simple Recursive Procedure