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Hamilton-connectivity of 3-Domination Critical Graphs with α = δ  +  2

✍ Scribed by Yaojun Chen; Feng Tian; Yunqing Zhang

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
208 KB
Volume
23
Category
Article
ISSN
0195-6698

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✦ Synopsis

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 connected 3-domination critical graph G is Hamilton-connected if and only if τ (G) > 1 and showed the conjecture is true when α ≤ δ. In this paper, by using a closure operation defined by Bondy and Chvátal, we show the conjecture is true when α = δ + 2.

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