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MIPT Interdepartmental Seminar on Discrete Mathematics
March 17, 2016 18:30, Dolgoprudnyi, Main building MIPT, room 113
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Extremal results for Berge-hypergraphs
D. Gerbner |
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Abstract:
Joint work with Cory Palmer
Let G be a graph and \mathcal{H} be a hypergraph both on the same vertex set. We say that \mathcal{H} is a Berge-G if there is a bijection f : E(G) -> E(\mathcal{H}) such that for e \in E(G) we have e \subset f(e). This generalizes the established definitions of «Berge path» and «Berge cycle» to general graphs. For a fixed graph G we examine the maximum possible size (i.e. the sum of the cardinality of each edge) of a hypergraph with no Berge-G as a subhypergraph.
In the present talk we prove general bounds for this maximum when G is an arbitrary graph. We also consider the specific case when G is a complete bipartite graph and prove an analogue of the Kővári-Sós-Turán theorem.
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