Claw-free graphs with complete closure Original Research Article

We study some properties of the closure concept in claw-free graphs that was introduced by the first author. It is known that G is hamiltonian if and only if its closure is hamiltonian, but, on the other hand, there are infinite 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.