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Title: Codiameters of 3-domination critical graphs with toughness more than one
Authors: Cheng, T. C. Edwin
Chen, Yaojun
Ng, Chi-to Daniel
Subjects: Domination-critical graph
Issue Date: 28-Mar-2009
Publisher: Elsevier
Source: Discrete mathematics, Mar. 2009, v. 309, no. 5, p. 1067-1078.
Abstract: A graph G is 3-domination-critical (3-critical, for short), if its domination number γ is 3 and the addition of any edge decreases γ by 1. In this paper, we show that every 3-critical graph with independence number 4 and minimum degree 3 is Hamilton-connected. Combining the result with those in [Y.J. Chen, F. Tian, B. Wei, Hamilton-connectivity of 3-domination critical graphs with α≤δ, Discrete Mathematics 271 (2003) 1–12; Y.J. Chen, F. Tian, Y.Q. Zhang, Hamilton-connectivity of 3-domination critical graphs with α=δ+2, European Journal of Combinatorics 23 (2002) 777–784; Y.J. Chen, T.C.E. Cheng, C.T. Ng, Hamilton-connectivity of 3-domination critical graphs with α=δ+1≥5, Discrete Mathematics 308 (2008) (in press)], we solve the following conjecture: a connected 3-critical graph G is Hamilton-connected if and only if τ(G)>1, where τ(G) is the toughness of G.
Rights: Discrete Mathematics © 2007 Elsevier B.V. The journal web site is located at
Type: Journal/Magazine Article
DOI: 10.1016/j.disc.2007.11.061
ISSN: 0012-365X
Appears in Collections:LMS Journal/Magazine Articles

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