%0 Journal Article %T A class of perfectly contractile graphs %A Fr¨¦d¨¦ric Maffray %A Nicolas Trotignon %J Mathematics %D 2013 %I arXiv %R 10.1016/j.jctb.2005.06.011 %X We consider the class ${\cal A}$ of graphs that contain no odd hole, no antihole, and no "prism" (a graph consisting of two disjoint triangles with three disjoint paths between them). We prove that every graph $G\in{\cal A}$ different from a clique has an "even pair" (two vertices that are not joined by a chordless path of odd length), as conjectured by Everett and Reed [see the chapter "Even pairs" in the book {\it Perfect Graphs}, J.L. Ram\'{\i}rez-Alfons\'{\i}n and B.A. Reed, eds., Wiley Interscience, 2001]. Our proof is a polynomial-time algorithm that produces an even pair with the additional property that the contraction of this pair yields a graph in ${\cal A}$. This entails a polynomial-time algorithm, based on successively contracting even pairs, to color optimally every graph in ${\cal A}$. This generalizes several results concerning some classical families of perfect graphs. %U http://arxiv.org/abs/1309.0438v1