Existence of a spanning tree having small diameter

In this paper, we prove that for a sufficiently large integer d and a connected graph G, if vertical bar V (G)vertical bar < (d+2)(delta(G)+1)/3, then there exists a spanning tree T of G such that diam(T) <= d. (C) 2021 Elsevier B.V. All rights reserved.

Automated summary

In this paper, it is proven that for a sufficiently large integer d and a connected graph G, if the number of vertices in G is less than (d+2)(delta(G)+1)/3, then there exists a spanning tree T of G such that the diameter of T is at most d.