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Hamilton-connectivity of 3-domination-critical graphs with α⩽δ

✍ Scribed by Yaojun Chen; Feng Tian; Bing Wei

Book ID
108315866
Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
296 KB
Volume
271
Category
Article
ISSN
0012-365X

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A graph G is 3-domination critical if its domination number γ is 3 and the addition of any edge decreases γ by 1. It was proved by Favaron et al. that α ≤ δ + 2 for any connected 3-domination critical graph. Denote by τ (G) the toughness of a graph G. Recently Chen et al. conjectured that a connecte

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## Abstract A graph __G__ is 3‐domination critical if its domination number γ is 3 and the addition of any edge decreases γ by 1. Let __G__ be a 3‐connected 3‐domination critical graph of order __n__. In this paper, we show that there is a path of length at least __n__−2 between any two distinct ve