A new proof of Wojcickaʹs conjecture Original Research Article

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 Hansonʹs (J. Combin. Math. Combin. Comput. 13 (1993) 121–128) and Bondy-Chvátalʹs (Discrete Math. 15(1976) 111–135) closure operations.