Claw-free graphs with complete closure

Zdeněk Ryjáček, Akira Saito, R.H Schelp
2001 Discrete Mathematics  
We study some properties of the closure concept in claw-free graphs that was introduced by the ÿrst author. It is known that G is hamiltonian if and only if its closure is hamiltonian, but, on the other hand, there are inÿnite classes of non-pancyclic graphs with pancyclic closure. We show several structural properties of claw-free graphs with complete closure and their clique cutsets and, using these results, we prove that every claw-free graph on n vertices with complete closure contains a cycle of length n − 1.
doi:10.1016/s0012-365x(00)00451-9 fatcat:q6xvs5b36jgw7ljkwcoa4dgv7m