  Sivaraman conjectured that if $G$ is a graph with no induced even cycle then
there exist sets $X_1, X_2 \subseteq V(G)$ satisfying $V(G) = X_1 \cup X_2$
such that the induced graphs $G[X_1]$ and $G[X_2]$ are both chordal. We prove
this conjecture in the special case where $G$ contains no sector wheel, namely,
a pair $(H, w)$ where $H$ is an induced cycle of $G$ and $w$ is a vertex in
$V(G) \setminus V(H)$ such that $N(w) \cap H$ is either $V(H)$ or a path with
at least three vertices.
