Planar Hamiltonian chordal graphs are cycle extendable (Q1850025)

A graph \(G\) is cycle extendable if each cycle of \(G\) is contained in a cycle with one additional vertex and \(G\) has at least one cycle, and \(G\) is chordal if each cycle with at least four vertices has a chord. \textit{G. R. T. Hendry} [Discrete Math. 85, 59-72 (1990; Zbl 0714.05038)] conjectured that a Hamiltonian chordal graph is cycle extendable. Support for this conjecture is given by proving that every planar Hamiltonian chordal graph is cycle extendable.