# 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}
}
• Published 15 July 2020
• Mathematics
• Discret. Math. Theor. Comput. Sci.
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…
1 Citations

## Figures from this paper

• Mathematics
SIAM 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.

## References

SHOWING 1-10 OF 14 REFERENCES

• Mathematics
SIAM J. Discret. Math.
• 2015
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.
• J. Bondy
• Mathematics
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.