Mittagsseminar (in cooperation with A. Steger, D. Steurer and B. Sudakov)

Date and Time: Tuesday, June 11, 2013, 12:15 pm

Duration: 30 minutes

Location: OAT S15/S16/S17

Speaker: Katarzyna Mieczkowska (Adam Mickiewicz University)

On Erdos' conjecture on matchings in hypergraphs

In 1959 Erdos and Gallai determined the minimum number of edges in a graph, which guarantees the existence of a matching of a given size. A few years later the following more general question was raised: what is the maximum possible number of edges in a k-uniform hypergraph on n vertices in which the largest matching has s edges. In 1965 Erdos conjectured that the optimal case is when the hypergraph is either a clique, or the complement of a clique. Erdos' claim has not been verified so far and has been confirmed only for a handful of special cases. In the talk we survey recent results on Erdos' conjecture and comment on some other related problems.

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