Transitive orientations in bull-reducible Berge graphs

Authors:
Celina de Figueiredo;Frédéric Maffray;Cláudia Villela Maciel
Affiliations:
Universidade Federal do Rio de Janeiro, Rio de Janeiro, Brazil;C.N.R.S., Laboratoire G-SCOP, Grenoble, France;Universidade Federal Fluminense, Niteroi, RJ, Brazil
Venue:
Discrete Applied Mathematics
Year:
2011

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Abstract

A bull is a graph with five vertices r,y,x,z,s and five edges ry, yx, yz, xz, zs. A graph G is bull-reducible if every vertex of G lies in at most one bull of G. We prove that every bull-reducible Berge graph G that contains no antihole is weakly chordal, or has a homogeneous set, or is transitively orientable. This yields a fast polynomial time algorithm to color the vertices of such a graph exactly.