Proving graph un-colorability with a consistency check of CSP

In this paper, we approach a derivation of the fifth challenge presented on IJCAI 1997 (Selman et al., 1997), that is to detect inconsistency by means of incomplete methods. Whereas this problem is of considerable interest, no significant contribution has emerged since 1997. In order to treat this matter, we review Gaur et al. (1997) that showed how to detect unsatisfiable CSP instances by coloring a graph. We observe that this approach doesn't seem to offer the expected prospects. Anyway, we exploit a similar process that permits to prove graph uncolorability by a CSP consistency check