Improved Exact Algorithms for Counting 3- and 4-Colorings

  • Fedor V. Fomin
  • Serge Gaspers
  • Saket Saurabh
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4598)


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

  • running in time O(1.7272 n ) for deciding if a graph is 4-colorable

  • running in time O(1.6262 n ) and O(1.9464 n ) for counting the number of k-colorings for k = 3 and 4 respectively.


Search Tree Chromatic Number Exact Algorithm Vertex Cover Graph Coloring 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Fedor V. Fomin
    • 1
  • Serge Gaspers
    • 1
  • Saket Saurabh
    • 1
    • 2
  1. 1.Department of Informatics, University of Bergen, N-5020 BergenNorway
  2. 2.The Institute of Mathematical Sciences, Chennai 600 113India

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