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# Robust properties of graphs (Asaf Ferber, UC Irvine)

## March 21, 2023 @ 12:15 pm - 1:10 pm

In this talk we will consider some notions of `robustness’ of graph/hypergraph properties. We will survey some existing results and will try to emphasize the following new result (joint with Adva Mond and Kaarel Haenni): The binomial random digraph $D_{n,p}$ typically contains the minimum between the minimum out- and in-degrees many edge-disjoint Hamilton cycles, given that $p\geq \log^C n/n$. The result is optimal up to log factors.