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    Hamiltonian chordal graphs are not cycle extendible

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    In 1990, Hendry conjectured that every Hamiltonian chordal graph is cycle extendible; that is, the vertices of any non-Hamiltonian cycle are contained in a cycle of length one greater. We disprove this conjecture by constructing counterexamples on nn vertices for any n≥15n \geq 15. Furthermore, we show that there exist counterexamples where the ratio of the length of a non-extendible cycle to the total number of vertices can be made arbitrarily small. We then consider cycle extendibility in Hamiltonian chordal graphs where certain induced subgraphs are forbidden, notably PnP_n and the bull.Comment: Some results from Section 3 were incorrect and have been removed. To appear in SIAM Journal on Discrete Mathematic
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