  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.
