A Note on the Degree Condition of Completely Independent Spanning Trees

Abstract

Given a graph G, a set of spanning trees of G are completely independent if for any vertices x and y, the paths connecting them on these trees have neither vertex nor edge in common, except x and y. In this paper, we prove that for graphs of order n, with n ≥ 6, if the minimum degree is at least n-2, then there are at least ⌊n/3⌋ completely independent spanning trees.