Solving 3-Colouring via 2SAT

  • Guillermo De Ita
  • César Bautista
  • Luis C. Altamirano
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6718)

Abstract

The 3-Colouring of a graph is a classic NP-complete problem. We show that some solutions for the 3-Colouring can be built in polynomial time based on the number of basic cycles existing in the graph. For this, we design a reduction from proper 3-Colouring of a graph G to a 2-CF Boolean formula F G , where the number of clauses in F G depends on the number of basic cycles in G. Any model of F G provides a proper 3-Colouring of G. Thus, F G is a logical pattern whose models codify proper 3-Colouring of the graph G.

Keywords

3-Colouring SAT Problem Efficient Computing 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Guillermo De Ita
    • 1
  • César Bautista
    • 1
  • Luis C. Altamirano
    • 1
  1. 1.Computer SciencesUniversidad Autónoma de PueblaMéxico

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