In 1973 Bermond, Germa, Heydemann and Sotteau conjectured that if n divides ( n k ) , then the complete k-uniform hypergraph on n vertices has a decomposition into Hamilton Berge cycles. Here a Berge cycle consists of an alternating sequence v1, e1, v2, . . . , vn, en of distinct vertices vi and distinct edges ei so that each ei contains vi and vi+1. So the divisibility condition is clearly nec...

We give some improvements on the BKT inequality, an inequality for perfect systems of difference sets due to Bermond, Kotzig, and Turgeon, and consider, in particular, their implications for the critical case in which the BKT inequality holds with equality.

This work deals with a generalization of the Cartesian product of graphs, the product graph Gm ∗Gp introduced by Bermond et al. [J.C. Bermond, C. Delorme, G. Farhi, Large graphs with givendegree anddiameter II, J. Combin. Theory, Series B 36 (1984), 32–48]. The connectivity of these product graphs is approached by studying the k-restricted edge-connectivity, which is defined as the minimum numb...

This paper considers the wavelength assignment problem for Cartesian product networks with multi-hops. An upper bound of the (uniform) wavelength index for Cartesian product networks with single-hop is established. This result leads to a consequence for the nth power of an arbitrary network with k-hops. In particular, if k = 1, this bound partially generalizes the results of Pankaj [R.K. Pankaj...

structural studies of literary works, which seek to examine the inner textual elements and to discover their connections, provide the grounds for better understanding the essence of literature and by presenting the devices of creating excellent literature can help us to expand the patterns of processing a literary work. a number of structural critics have dealt with the narrative forms by study...

In 1996, J-C bermond, T. Kodate, N. Marlin and S. Perennes conjectured that the set of fixed points of some complete rotation of the toroidal mesh is not separating. They also conjectured that the set of fixed points of any complete rotation of any Cayley digraph is not separating. In this paper, we prove the first conjecture and disprove the second one.

Let $n(k, d)$ be the order of largest undirected graphs maximum degree $k$ and diameter $d$, let $M(k,d)$ corresponding Moore bound. In this paper, we give a positive answer to question Bermond Bollob\'as concerning Degree/Diameter Problem: Given integer $c>0$, does there exist pair such that d)\leq M(k,d)-c?$

A (λKv, G)-design is a partition of the edges of λKv into subgraphs each of which is isomorphic to G. In this paper, we completely solve the case when G = G18 (G18 is notation from Bermond, Huang, Rosa and Sotteau, Ars Combin. 10 (1980), 211–254) and prove that the necessary condition λv(v− 1) ≡ 0 (mod 14) for the existence of a (λKv, G18)-design with any positive integer λ is also sufficient e...

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