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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## 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
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,