On the height of independent spanning trees of a k-connected k-regular graph

Abstract

A set of paths connecting two vertices in a graph is said to be internally disjoint if and only if any pair of paths in the set has no common vertex expect the two end vertices. Considering a graph G=(V,E), a tree T is called a spanning tree of G if T is a subgraph of G and T contains all vertices in V. Two spanning trees of Gare said to be intependent if they are rooted at the same vertex, say r, and for each vertex v {r}, the two paths from r to v, one path in each tree, are internally disjoint. A set of spanning trees of a graph is daid to be independent if they are pairwise independent.