Claw-free graphs with complete closure
نویسندگان
چکیده
We study some properties of the closure concept in claw-free graphs that was introduced by the rst author. It is known that G is hamiltonian if and only if its closure is hamiltonian, but, on the other hand, there are innnite 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.
منابع مشابه
On cycle lengths in claw-free graphs with complete closure
We show a construction that gives an infinite family of claw-free graphs of connectivity κ = 2, 3, 4, 5 with complete closure and without a cycle of a given fixed length. This construction disproves a conjecture by the first author, A. Saito and R.H. Schelp.
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عنوان ژورنال:
- Discrete Mathematics
دوره 236 شماره
صفحات -
تاریخ انتشار 2001