Solving 3-Colouring via 2SAT
نویسندگان
چکیده
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 FG, where the number of clauses in FG depends on the number of basic cycles in G. Any model of FG provides a proper 3-Colouring of G. Thus, FG is a logical pattern whose models codify proper 3-Colouring of the graph G.
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