A new property of critical imperfect graphs and some consequences
European Journal of Combinatorics
Perfectly orderable graphs are quasi-parity graphs: A short proof
Discrete Mathematics
On the complexity of recognizing perfectly orderable graphs
Discrete Mathematics
Journal of Combinatorial Theory Series B
A fast algorithm for coloring Meyniel graphs
Journal of Combinatorial Theory Series B
Discrete Mathematics
About skew paritions in minimal imperfect graphs
Journal of Combinatorial Theory Series B
Combinatorica
Journal of Combinatorial Theory Series B
Theoretical Computer Science
Graph transformations preserving the stability number
Discrete Applied Mathematics
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We consider the class 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 ∈ 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 ["Even pairs", in: J.L. Ramírez-Alfonsín, B.A. Reed (eds.), Perfect Graphs, Wiley Interscience, New York, 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 A. This entails a polynomial-time algorithm, based on successively contracting even pairs, to color optimally every graph in A. This generalizes several results concerning some classical families of perfect graphs.