Trees with equal domination and tree-free domination numbers Original Research Article

The tree-free domination number γ(G;−Tk), k⩾2, of a graph G is the minimum cardinality of a dominating set S in G such that the subgraph 〈S〉 induced by S contains no tree on k vertices as a (not necessarily induced) subgraph (equivalently, each component of 〈S〉 has cardinality less than k). When k=2, the tree-free domination number is the independent domination number. We obtain a characterization of trees with equal domination and tree-free domination numbers. This generalizes a result of Cockayne et al. (A characterisation of (γ,i)-trees. J. Graph Theory 34(4) (2000) 277–292).