We present some characterizations for the wrapped butterfly, a class of useful network models in parallel processing. Our characterizations are parallel to the characterization of Bermond et al. for the (ordinary) butterfly. But our approach seems more natural and provides some more insight. In the course of our study, we also give a slight improvement of a result of Beineke et al. which charac...

In 1981, Bermond and Thomassen conjectured that every digraph with minimum out-degree at least 2k − 1 contains k disjoint cycles. This conjecture is trivial for k = 1, and was established for k = 2 by Thomassen in 1983. We verify it for the next case, by proving that every digraph with minimum out-degree at least five contains three disjoint cycles. To show this, we improve Thomassen’s result b...

5 We prove that every tournament with minimum out-degree at least 2k− 1 contains k disjoint 6 3-cycles. This provides additional support for the conjecture by Bermond and Thomassen that 7 every digraph D of minimum out-degree 2k − 1 contains k vertex disjoint cycles. We also prove 8 that for every > 0, when k is large enough, every tournament with minimum out-degree at least 9 (1.5+ )k contains...

The partial line digraph technique was introduced in [7] in order to construct digraphs with a minimum diameter, maximum connectivity, and good expandability. To find a new method to construct directed hypergraphs with a minimum diameter, we present in this paper an adaptation of that technique to directed hypergraphs. Directed hypergraphs are used as models for interconnection networks whose v...

A triangle is a family of three sets A,B,C such that A∩B, B∩C, C∩A are each nonempty, and A ∩ B ∩ C = ∅. Let A be a family of r-element subsets of an n-element set, containing no triangle. Our main result implies that for r ≥ 3 and n ≥ 3r/2, we have |A| ≤ ( n−1 r−1 ) . This settles a longstanding conjecture of Erdős [7], by improving on earlier results of Bermond, Chvátal, Frankl, and Füredi. W...

Let r be a positive integer. Consider r-regular graphs in which no induced subgraph on four vertices is an independent pair of edges. The number v of vertices in such a graph does not exceed 5r/2; this proves a conjecture of Bermond. More generally, it is conjectured that if v > 2r, then the ratio v/r must be a rational number of the form 2 + 1/(2k). This is proved for v/r > 21 _ ~ . The extrem...

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As it is introduced by Bermond, Kodate, and Prennes, some Cayley graphs, including most popular models for interconnection networks, admit a special auto-morphism, called complete rotation. Such an automorphism is often used to derive algorithms or properties of the underlying graph. For example, optimal gossiping algorithms can be easily designed, and the constructions of the best known edge d...