The foundations of incomplete contracts have been questioned using or extending the subgame perfect implementation approach of Moore and Repullo (1988). We consider the robustness of subgame perfect implementation to the introduction of small amounts of asymmetric information. We show that Moore-Repullo mechanisms may not yield (even approximately) truthful revelation in pure or totally mixed s...

We derive some Moore-like bounds for multipartite digraphs, which extend those of bipartite digraphs, assuming that every vertex of a given partite set is adjacent to the same number of vertices (δ) in each of the other independent sets. We determine when a Moore multipartite digraph is weakly distanceregular. Within this framework, some necessary conditions for the existence of a Moore r-parti...

This note gives a “Zorn’s Lemma” style proof that any two bases in a vector space have the same cardinality. One of the most fundamental notions in linear algebra is that of a basis: A subset B of a vector space V is a basis if every element of V is a unique linear combination of elements of B. The following theorem of Georg Hamel expresses one of the most important aspects of this definition. ...

Probably the two best-known exact string matching algorithms are the linear-time algorithm of Knuth, Morris and Pratt (KMP), and the fast on average algorithm of Boyer and Moore (BM). The efficiency of these algorithms is based on using a suitable failure function. When a mismatch occurs in the currently inspected text position, the purpose of a failure function is to tell how many positions th...

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...

Almost Moore digraphs appear in the context of the degree/diameter problem as a class of extremal directed graphs, in the sense that their order is one less than the unattainable Moore bound M(d, k) = 1 + d + · · · + dk, where d > 1 and k > 1 denote the maximum out-degree and diameter, respectively. So far, the problem of their existence has only been solved when d = 2, 3 or k = 2. In this pape...

Almost Moore digraphs appear in the context of the degree/diameter problem as a class of extremal directed graphs, in the sense that their order is one less than the unattainable Moore bound M(d, k) = 1 + d + · · · + d, where d > 1 and k > 1 denote the maximum out-degree and diameter, respectively. So far, the problem of their existence has only been solved when d = 2, 3 or k = 2, 3. In this pa...