For graphs with maximum degree A and diameter D, an upper bound on the number of vertices is 1 + AxF:-,‘(A 1)‘. This bound is called the Moore bound for graphs and the graphs that attain it are called Moore graphs. Similar bounds for directed graphs and for hypergraphs have been defined and the existence of directed Moore graphs and of Moore hypergraphs has been studied. In this article, we def...

Sometimes the bad character heuristics fails. In the following situation the comparison a-b causes a mismatch. An alignment of the rightmost occurence of the pattern symbol a with the text symbol a would produce a negative shift. Instead, a shift by 1 would be possible. However, in this case it is better to derive the maximum possible shift distance from the structure of the pattern. This metho...

In the context of the degree/diameter problem for directed graphs, it is known that the number of vertices of a strongly connected bipartite digraph satisfies a Moore-like bound in terms of its diameter k and the maximum out-degrees (d1; d2) of its partite sets of vertices. It has been proved that, when d1d2 > 1, the digraphs attaining such a bound, called Moore bipartite digraphs, only exist w...

For the relevant literature and most of the definitions and conventions the reader is referred to [1]. The next section contains an explicit description of the (reduced) characteristic polynomial of L4(s, t), and it is shown that this polynomial admits a decomposition into two closely related factors of degree 2 each. In Section 3 it is first shown that at least one of these factors must be red...

Given a set Un = {0, 1, ..., n− 1}, a collection M of subsets of Un that is closed under intersection and contains Un is known as a Moore family. The set of Moore families for a xed n is in bijection with the set of Moore co-families (union-closed families containing the empty set) denoted itself Mn. In this paper, we propose for the rst time a recursive de nition of the set of Moore co-familie...