Even pairs in square-free Berge graphs

Frédéric Maffray (1)

1 G-SCOP_OC - Optimisation Combinatoire

We consider the class of Berge graphs that contain no odd prism and no square (cycle on four vertices). We prove that every graph G in this class either is a clique or has an even pair, as conjectured by Everett and Reed. This result is used to devise a polynomial-time algorithm to color optimally every graph in this class.

Domaines: Mathématique discrète [cs.DM]

Frédéric Maffray. Even pairs in square-free Berge graphs. Electronic Notes in Discrete Mathematics, 2015, The Eight European Conference on Combinatorics, Graph Theory and Applications, EuroComb 2015, 49, pp.173-180. ⟨10.1016/j.endm.2015.06.026⟩. ⟨hal-01387216⟩