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On locally k-critically n-connected graphs

✍ Scribed by Jianji Su

Publisher: Elsevier Science
Year: 1993
Tongue: English
Weight: 479 KB
Volume: 120
Category: Article
ISSN: 0012-365X
DOI: 10.1016/0012-365x(93)90575-e

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✦ Synopsis

Su, J., On locally k-critically n-connected graphs, Discrete Mathematics 120 (1993) 183-190. Let 0 # W'g V(G). The graph G is called a W-locally k-critically n-connected graph or simply a W-locally (n, k)-graph, if for all V'G W with 1 V'I 6 k and each fragment F of G we have that K(G-V')=n-1 V' and Fn W#@I. In this paper we prove that every non-complete W-locally (n, k)-graph has (2k+2) distinct fragments and 1 WI >2k+2. From this result it follows that: (1) Let G be a non-complete (n. k)-graph. If all ends of G are proper, then G has (2k + 2) pairwise disjoint ends.

(2) Slater's conjecture on (n, k)-graphs holds, i.e., the complete graph Kn+ 1 is the unique (n, k)graph for 2k>n.

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