Independence and hamiltonicity in 3-domination-critical graphs
Odile Favaron, Feng Tian, Lei Zhang · Journal of Graph Theory · 1997
Let δ, γ, i and α be respectively the minimum degree, the domination number, the independent domination number and the independence number of a graph G. The graph G is 3-γ-critical if γ = 3 and the addition of any edge decreases γ by 1. It was conjectured that any connected 3-γ-critical graph satisfies i = γ, and is hamiltonian if δ ≥ 2. We show here that every connected 3-γ-critical graph G with γ ≥ 2 satisfies α ≤ δ + 2; if α = δ + 2 then i = γ; while if α ≤ δ + 1 then G is hamiltonian. © 1997 Wiley & Sons, Inc. J Graph Theory 25: 173–184, 1997