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Sufficient conditions for a graph to be λk-optimal with given girth and diameter

✍ Scribed by Zhao Zhang; Qinghai Liu


Publisher
John Wiley and Sons
Year
2009
Tongue
English
Weight
198 KB
Volume
55
Category
Article
ISSN
0028-3045

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Sufficient conditions for graphs to be λ
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## Abstract The restricted‐edge‐connectivity of a graph __G__, denoted by λ′(__G__), is defined as the minimum cardinality over all edge‐cuts __S__ of __G__, where __G__‐__S__ contains no isolated vertices. The graph __G__ is called λ′‐optimal, if λ′(__G__) = ξ(__G__), where ξ(__G__) is the minimum

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We prove the following conjecture of Broersma and Veldman: A connected, locally k-connected K,,-free graph is k-hamiltonian if and only if it is (k + 2)-connected ( k L 1). We use [ 11 for basic terminology and notation, and consider simple graphs only. Let G be a graph. By V(G) and E(G) we denote,