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Closure and Hamiltonian-connectivity of claw-free graphs

✍ Scribed by Béla Bollobás; Oliver Riordan; Zdeněk Ryjáček; Akira Saito; R.H. Schelp


Book ID
108316280
Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
756 KB
Volume
195
Category
Article
ISSN
0012-365X

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Closure and stable Hamiltonian propertie
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In the class of k-connected claw-free graphs, we study the stability of some Hamiltonian properties under a closure operation introduced by the third author. We prove that (i) the properties of pancyclicity, vertex pancyclicity and cycle extendability are not stable for any k (i.e., for any of these

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## Abstract In this paper, we show that every 3‐connected claw‐free graph on n vertices with δ ≥ (__n__ + 5)/5 is hamiltonian. © 1993 John Wiley & Sons, Inc.

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## Abstract M. Matthews and D. Sumner have proved that of __G__ is a 2‐connected claw‐free graph of order __n__ such that δ ≧ (__n__ − 2)/3, then __G__ is hamiltonian. We prove that the bound for the minimum degree δ can be reduced to __n__/4 under the additional condition that __G__ is not in __F_

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A graph G is N 2 -locally connected if for every vertex v in G, the edges not incident with v but having at least one end adjacent to v in G induce a connected graph. In 1990, Ryja ´c ˇek conjectured that every 3-connected N 2 -locally connected claw-free graph is Hamiltonian. This conjecture is pro