Planar Hamiltonian chordal graphs are cycle extendable Original Research Article

A cycle C in a graph G is extendable if there exists a cycle C′ in G such that V(C)⊆V(C′) and |V(C′)|=|V(C)|+1. A graph G is cycle extendable if G contains at least one cycle and every non-Hamiltonian cycle in G is extendable. Hendry (Discrete Math. 85 (1990) 59) asked if every Hamiltonian chordal graph is cycle extendable. We prove that every planar Hamiltonian chordal graph is cycle extendable.