Transitive orientations in bull-reducible Berge graphs

Details Transitive orientations in bull-reducible Berge graphs Transitive orientations in bull-reducible Berge graphs

2008-10-24

arxiv.org/abs/0810.4522v1

Mathematics

Combinatorics

Scientific paper

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.

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