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Stable and k-stable graph properties
by
Zdeněk Ryjáček
University of West Bohemia, Pilsen, Czech Republic
For a claw-free graph G, cl(G) denotes its closure (obtained by local completions at locally connected vertices). More generally, for k ≥ 1, the k-closure clk(G) of G is obtained from G by local completions at locally k-connected vertices. A class of graphs C is said to be k-stable (under the k-closure) if G ∈ C ⇒ clk(G) ∈ C. A property P is said to be k-stable in a k-stable class C if, for any G ∈ C, G has P ⇔ clk(G) has P. Similarly, a graph invariant p is said to be k-stable in C if, for any G ∈ C, p(G)=p(clk(G)).
In the talk we mention some known results on stability of graph properties under clk(G). As a recent application it is shown (joint work with Petr Vrána, Plzen, ) that every 7-connected claw-free graph is Hamilton-connected.
Date received: April 18, 2008
Copyright © 2008 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cawn-61.