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 no vertex of G lies in two bulls. 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 exactly the vertices of such a graph.
@article{arxiv.0810.4522,
title = {Transitive orientations in bull-reducible Berge graphs},
author = {Celina de Figueiredo and Frederic Maffray and Claudia Villela Maciel},
journal= {arXiv preprint arXiv:0810.4522},
year = {2008}
}