Graphs with no even holes and no sector wheels are the union of two chordal graphs

Sivaraman (2020) conjectured that if G is a graph with no induced even cycle then there exist sets X₁,X₂⊆V(G) satisfying V(G)=X₁∪X₂ such that the induced graphs G[X₁] and G[X₂] 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)∖V(H) such that N(w)∩H is either V(H) or a path with at least three vertices.