On the largest tree of given maximum degree in a connected graph

Abstract

We prove that every connected graph G contains a tree T of maximum degree at most k that either spans G or has order at least k(G) + 1, where (G) is the minimum degree of G. This generalizes and unifies earlier results of Bermond [1] and Win [7]. We also show that the square of a connected graph contains a spanning tree of maximum degree at most three.