## Hamiltonian chordal graphs are not cycle extendible

- Manuel Lafond, Ben Seamone
- SIAM J. Discrete Math.
- 2015

@article{Ryjcek1994AlmostCG, title={Almost claw-free graphs}, author={Zdenek Ryj{\'a}cek}, journal={Journal of Graph Theory}, year={1994}, volume={18}, pages={469-477} }

- Published 1994 in Journal of Graph Theory
DOI:10.1002/jgt.3190180505

We say that G is almost claw-free if the vertices that are centers of induced claws (K,J in G are independent and their neighborhoods are 2-dominated. Clearly, every claw-free graph is almost claw-free. It is shown that (i) every even connected almost claw-free graph has a perfect matching and (ii) every nontrivial locally connected Kl,4-free almost claw-free graph is fully cycle extendable.

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