A new proof of Wojcicka's conjecture

Authors:
Yaojun Chen;Feng Tian
Affiliations:
Department of Mathematics, Nanjing University, Nanjing 210093, China;Institute of Systems Science, Academy of Mathematics and Systems Sciences, Chinese Academy of Sciences, Beijing 100080, China
Venue:
Discrete Applied Mathematics
Year:
2003

Citing 5
Cited 1

Hamiltonian properties of domination-critical graphs

Journal of Graph Theory
Independence and hamiltonicity in 3-domination-critical graphs

Journal of Graph Theory
Hamiltonicity in 3-domination-critical graphs with &agr; = &dgr; + 2

Discrete Applied Mathematics
Some properties of 3-domination-critical graphs

Discrete Mathematics
Independence and connectivity in 3-domination-critical graphs

Discrete Mathematics

Hamilton-connectivity of 3-domination critical graphs with α = δ + 2

European Journal of Combinatorics

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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. Wojcicka conjectured that every 3-domination-critical graph with δ ≥ 2 has a hamiltonian cycle (J. Graph Theory 14 (1990) 205-215). The conjecture had been proved and its proof consists of two parts: the case α ≤ δ + 1 (J. Graph Theory 25 (1997) 173-184) and the case α = δ + 2 (Discrete Appl. Math. 92 (1999) 57-70). In this paper, we give a new and simple proof of the conjecture by using Hanson's (J. Combin. Math. Combin. Comput. 13 (1993) 121-128) and Bondy-Chvátal's (Discrete Math. 15(1976) 111-135) closure operations.