We present a simple and e cient dictionary with worst case constant lookup time, equaling the theoretical performance of the classic dynamic perfect hashing scheme of Dietzfelbinger et al. (Dynamic perfect hashing: Upper and lower bounds. SIAM J. Comput., 23(4):738 761, 1994). The space usage is similar to that of binary search trees, i.e., three words per key on average. The practicality of th...

A graph is Berge if no induced subgraph of it is an odd cycle of length at least five or the complement of one. In joint work with Robertson, Seymour, and Thomas we recently proved the Strong Perfect Graph Theorem, which was a conjecture about the chromatic number of Berge graphs. The proof consisted of showing that every Berge graph either belongs to one of a few basic classes, or admits one o...

Normal graphs are defined in terms of cross-intersecting set families: a graph is normal if it admits a clique cover Q and a stable set cover S s.t. every clique in Q intersects every stable set in S. Normal graphs can be considered as closure of perfect graphs by means of co-normal products (K ̈orner [6]) and graph entropy (Czisz ́ar et al. [5]). Perfect graphs have been recently characterized a...

Abstract We define the notion of a specialization morphism from locally noetherian analytic adic space to scheme. This captures (classical) associated with formal There is well-behaved theory compactifications and it turns out that classical proper in this setup. As an application, we show nearby cycles functor commutes lower shriek great generality.

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