# Construct Independent Spanning Trees on Chordal Rings with Multiple Chords

• Shyue-Ming Tang
Conference paper
Part of the Smart Innovation, Systems and Technologies book series (SIST, volume 20)

## Abstract

Two spanning trees of a given graph G = (V, E) are said to be independent if they are rooted at the same vertex, say r, and for each vertex v ∈ V ∖ {r} two paths from r to v, one path in each tree, are internally disjoint. A set of spanning trees of G is said to be independent if they are pairwise independent. In 1989, Zehavi and Itai have conjectured that any k-connected graph has k independent spanning trees rooted at an arbitrary vertex. This conjecture is still open for k > 4.

A chordal ring is a ring network with extra links (chords) at each vertex. Y. Iwasaki et al. have proposed an algorithm to construct independent spanning trees on a chordal ring of degree four. (See [Y. Iwasaki et al., Independent panning trees of chordal rings, Information Processing Letters 69 (1999) 155-160].) In this paper, we shall propose an algorithm to solve the independent spanning trees problem on chordal rings with multiple chords.

### Keywords

independent spanning trees chordal rings circulant graphs vertex-symmetric graphs internally disjoint paths fault-tolerant broadcasting

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