A forbidden pair for connected graphs to have spanning k‐trees

For an integer k ≥ 2, a k‐tree is a tree with maximum degree at most k. A k‐tree containing all vertices of a graph G is called a spanning k‐tree of G. In 2010, Ota and Sugiyama gave a forbidden induced subgraph condition for a graph to have a spanning k‐tree and they posed a conjecture that is stronger than their result. In this paper, we solve their conjecture.