U.S.-Polish Research on "Probabilistic Combinatorics"

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9406971 Rodl This U.S.-Polish Joint Cooperative Research in Probabilistic Combinatorics is between Drs. Vojtech Rodl and Dwight Duffus of Emory University and Drs. Michal Karonski, Tomasz Luczak, and Andrzej Rucinski of the Institute of the Department of Discrete Mathematics of Adam Mickiewicz University in Poznan. The problems addressed in this research belong to probabilistic combinatorics. They either deal with properties of random structures or are expected to be solved by probabilistic means. The Polish investigators are experts in the theory of random graphs, which, besides its own interest, provides powerful tools for solving many hard problems. Specifically, the researchers will examine: (1) extremal and Ramsey type properties of random structures; (2) probabilistic approach to some extremal and Ramsey-type problems; (3) matchings in random graphs and hypergraphs; (4) phase transition in graph processes with bounded maximum degree; and (5) enumeration of order preserving maps. This proposed research in mathematics and computer science fulfills the program objectives of advancing science by enabling leading experts in the U.S. and Poland to combine complementary talents and pool research resources in areas of strong mutual interest and competence. ***