# Further results on Hendry's Conjecture

@article{Lafond2020FurtherRO, title={Further results on Hendry's Conjecture}, author={Manuel Lafond and Ben Seamone and Rezvan Sherkati}, journal={Discret. Math. Theor. Comput. Sci.}, year={2020}, volume={24} }

Recently, a conjecture due to Hendry was disproved which stated that every
Hamiltonian chordal graph is cycle extendible. Here we further explore the
conjecture, showing that it fails to hold even when a number of extra
conditions are imposed. In particular, we show that Hendry's Conjecture fails
for strongly chordal graphs, graphs with high connectivity, and if we relax the
definition of "cycle extendible" considerably. We also consider the original
conjecture from a subtree intersection model…

## One Citation

### Cycle Extendability of Hamiltonian Strongly Chordal Graphs

- MathematicsSIAM J. Discret. Math.
- 2021

These questions in the negative are resolved and two more graph classes are added to the list of cycle extendable graphs, namely, Hamiltonian $4$-leaf powers and Hamiltonian {4-FAN, $\overline{A}$}-free chordal graphs.

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This work disproves the conjecture 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, by constructing counterexamples on vertices for any $n$ vertices.

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As its name implies, this paper consists of observations on various topics in graph theory that stem from the concept of Hamiltonian cycle. We shall mainly adopt the notation and terminology of…

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- MathematicsSIAM J. Discret. Math.
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These questions in the negative are resolved and two more graph classes are added to the list of cycle extendable graphs, namely, Hamiltonian $4$-leaf powers and Hamiltonian {4-FAN, $\overline{A}$}-free chordal graphs.

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iii PUBLIC ABSTRACT v ACKNOWLEDGMENTS vii LIST OF FIGURES xi

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