A new proof of Wojcicka's conjecture ?
A graph G is 3-domination-critical if its domination number ? is 3 and the addition of any edge decreases ? by 1. Wojcicka conjectured that every 3-domination-critical graph with ??2 has a hamiltonian cycle (J. Graph Theory 14 (1990) 205215). The conjecture had been proved and its proof consists of two parts: the case ???+1 (J. Graph Theory 25 (1997) 173184) and the case ?=?+2 (Discrete Appl. Math. 92 (1999) 5770). In this paper, we give a new and simple proof of the conjecture by using Hanson's (J. Combin. Math. Combin. Comput. 13 (1993) 121128) and Bondy-Chvtal's (Discrete Math. 15(1976) 111135) closure operations.
hamiltonian cycle closure operation domination-critical graph