Forbidden subgraphs and the existence of spanning kk-trees

A kk-tree of a graph is a subtree with maximum degree at most kk. 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 kk-tree for k≥3k≥3. In this paper, we give a sufficient condition using the condition on forbidden subgraphs for a graph GG to have a spanning kk-tree.