Forbidden subgraphs and the existence of spanning -trees

A k -tree of a graph is a subtree with maximum degree at most k . Though forbidden subgraphs are a major tool to find a hamiltonian cycle or a hamiltonian path, there are only a few results using the condition on forbidden subgraphs to find a spanning k -tree for k ≥ 3 . In this paper, we give a sufficient condition using the condition on forbidden subgraphs for a graph G to have a spanning k -tree.