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június 19. (!!! CSÜTÖRTÖK !!!), !!! 11:00 !!!,
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Kalmár Intézet, Árpád tér, szemináriumi szoba (második emelet, a folyosó vége)

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Cory Palmer (Montana University): Extremal results for Berge-hypergraphs

Abs: Let H be a hypergraph and G be a graph. We say that H contains G if we can embed G into the vertex set of H such that each edge of G can be associated with a distinct edge of H containing it. We say H is G-free if it does not contain G. (When H is a graph this is the ordinary notion that H does not contain G as a subgraph).

We would like to determine the maximum possible size of the sum of the vertex degrees in an G-free hypergraph H on n vertices. (When H is a graph this maximum is twice the extremal number of G). Győri and Lemons showed that for 3-uniform hypergraphs, when G is an even cycle that this maximum has the same order as the extremal number of even cycle in graphs. Surprisingly, for cycles of length 2k+1 the parameter is the same order as for cycles of length 2k (this is significantly different from the extremal number of odd cycles in graphs).

We examine this question in a slightly more general setting and show that for any graph G, the maximum degree sum cannot behave too differently from the extremal number of G. We then focus on the particular case when G is a complete bipartite graph to get an analogue of the Kővari-Sós-Turán theorem. (joint work with D. Gerbner).

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Supported by TÁMOP-4.2.2.A-11/1/KONV-2012-0073, Telemedicine Oriented Research in the Fields of Mathematics, Informatics and Medical Sciences