On the largest tree of given maximum degree in a connected graph
Yair Caro, Ilia Krasikov, Y. Roditty · Journal of Graph Theory · 1991
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 kδ(G) + 1, where δ(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.