✦ LIBER ✦

Paths, cycles, and arc-connectivity in digraphs

✍ Scribed by Xiang-Ying Su

Publisher: John Wiley and Sons
Year: 1995
Tongue: English
Weight: 645 KB
Volume: 19
Category: Article
ISSN: 0364-9024
DOI: 10.1002/jgt.3190190307

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The purpose of this communication is to announce some slrfficient conditions on degrees and number of arcs to insure the existence of cycles and paths in directed graphs. We show that these results are the best possible. The proofs of the theorems can be found in [4].

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We show that for any vertex \(x\) of a \(d\)-regular bipartite digraph there are a vertex \(y\), in the other class of the bipartition, and \(d(x, y)\)-paths and \(d(y, x)\)-paths such that all \(2 d\) of them are pairwise arc-disjoint. This result generalizes a theorem of Hamidoune and Las Vergnas

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A digraph D is called a quasi-transitive digraph (QTD) if for any triple x,y,z of distinct vertices of D such that (x,y) and (y,z) are arcs of D there is at least one at': from x to z or from z to x. Solving a conjecture by Bangdensen and Huang (1995), Gutin (1995) described polynomial algorithms fo

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Cayley graphs arise naturally in computer science, in the study of word-hyperbolic groups and automatic groups, in change-ringing, in creating Escher-like repeating patterns in the hyperbolic plane, and in combinatorial designs. Moreover, Babai has shown that all graphs can be realized as an induced