Hamilton-connectivity of 3-domination critical graphs with α = δ + 1 ≥ 5

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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-domination critical graph with toughness more than one. It was proved that G is Hamilton-connected for the cases α ≤ δ [Y.J. Chen, F. Tian, B. Wei, Hamilton-connectivity of 3-domination critical graphs with α ≤ δ, Discrete Math. 271 (2003) 1-12] and α = δ + 2 [Y.J. Chen, F. Tian, Y.Q. Zhang, Hamilton-connectivity of 3-domination critical graphs with α = δ + 2, European J. Combin. 23 (2002) 777-784]. In this paper, we show G is Hamilton-connected for the case α = δ + 1 ≥ 5.
Original languageEnglish
Pages (from-to)1296-1307
Number of pages12
JournalDiscrete Mathematics
Volume308
Issue number7
DOIs
Publication statusPublished - 6 Apr 2008

Keywords

  • Domination-critical graph
  • Hamilton-connectivity

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics

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