Results 1 
3 of
3
Independent Spanning Trees With Small Depths in Iterated Line Digraphs
, 1997
"... . We show that the independent spanning tree conjecture on digraphs is true if we restrict ourselves to line digraphs. Also, we construct independent spanning trees with small depths in iterated line digraphs. From the results, we can obtain independent spanning trees with small depths in de Bruijn ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
. We show that the independent spanning tree conjecture on digraphs is true if we restrict ourselves to line digraphs. Also, we construct independent spanning trees with small depths in iterated line digraphs. From the results, we can obtain independent spanning trees with small depths in de Bruijn and Kautz digraphs that improve the previously known upper bounds on the depths. Keywords. independent spanning trees, line digraphs, vertexconnectivity, de Bruijn digraphs, Kautz digraphs, interconnection networks, broadcasting. 1 Introduction Unless stated otherwise each digraph of this paper is nite and may have loops but not multiarcs. Let G be a digraph. Then V (G) and A(G) denote the vertex set and the arc set of G, respectively. Let (u; v) 2 A(G). Then we say that u is adjacent to v, and v is adjacent from u. Also, it is said that (u; v) is incident to v and incident from u. Let (v; w) 2 A(G). Then we say that (u; v) is adjacent to (v; w), and (v; w) is adjacent from (u; v). Let ...
Parallel Construction of Independent Spanning Trees on Multidimensional Tori
 THE 24TH WORKSHOP ON COMBINATORIAL MATHEMATICS AND COMPUTATION THEORY
"... A set of spanning trees rooted at vertex r in G is called independent spanning trees (IST) if for each vertex v in G, v = r, the paths from v to r in any two trees are different and vertexdisjoint. If the connectivity of G is k, the IST problem is to construct k IST rooted at each vertex. The IST ..."
Abstract
 Add to MetaCart
A set of spanning trees rooted at vertex r in G is called independent spanning trees (IST) if for each vertex v in G, v = r, the paths from v to r in any two trees are different and vertexdisjoint. If the connectivity of G is k, the IST problem is to construct k IST rooted at each vertex. The IST problem has found applications in faulttolerant broadcasting, but it is still open for general graph with connectivity greater than four. Obokata et al. [IEICE Trans. Fundamentals of Electronics, Communications and Computer Sciences E79A (1996) 1894–1903] have proved that the IST problem can be solved on multidimensional tori. However, their construction algorithm forbids the possibility of parallel processing. In this paper, we shall propose a parallel algorithm that is based on the Latin square scheme to solve the IST problem on multidimensional tori.