Reducing the height of independent spanning trees in chordal rings

Abstract

This paper is concerned with a particular family of regular 4-connected graphs, called chordal rings. Chordal rings are a variation of ring networks. By adding extra two links (or chords) at each vertex in a ring network, the reliability and fault-tolerance of the network are enhanced. Two spanning trees on a graph are said to be independent if they are rooted at the same vertex, say r, and for each vertex v 6= r, the two paths from r to v, one path in each tree, are internally disjoint. A set of spanning trees on a given graph is said to be independent if they are pairwise independent. In 1999, Y. Iwasaki et al. proposed a linear time algorithm to find four independent spanning trees on a chordal ring. In this paper, we shall give new algorithms to generate four independent spanning trees with reduced height in each tree.