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 X 1 , X 2 subset of V ( G ) satisfying V ( G ) = X 1 boolean OR 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 contains no sector wheel, namely, a pair (H, H , w ) where H is an induced cycle of G and w is a vertex in V ( G ) \ V ( H ) such that N ( w ) boolean AND H is either V ( H ) or a path with at least three vertices. (c) 2024 Elsevier Ltd. All rights are reserved, including those for text and data mining, AI training, and similar technologies.