A new proof of Wojcicka's conjecture

A graph G is 3-domination-critical if its domination number gamma is 3 and the addition of any edge decreases gamma by 1. Wojcicka conjectured that every 3-domination-critical graph with delta greater than or equal to 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 alpha less than or equal to delta + I (J. Graph Theory 25 (1997) 173-184) and the case alpha = delta + 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-Chvatal's (Discrete Math. 15(1976) 111-135) closure operations. (C) 2002 Elsevier Science B.V. All rights reserved.