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. © 2011 Springer-Verlag Berlin Heidelberg.
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CITATION STYLE
De Ita, G., Bautista, C., & Altamirano, L. C. (2011). Solving 3-colouring via 2SAT. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 6718 LNCS, pp. 50–59). https://doi.org/10.1007/978-3-642-21587-2_6
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