Further results on Hendry's Conjecture

Recently, a conjecture due to Hendry which stated that every Hamiltonian chordal graph is cycle extendable was disproved. 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 one relaxes the definition of "cycle extendable" considerably. We also consider the original conjecture from a sub-tree intersection model point of view, showing that a result of Abuieda et al. is nearly best possible.