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

Date and Time: Thursday, November 16, 2023, 12:15 pm

Duration: 30 minutes

Location: CAB G51

Speaker: Zhihan Jin

Difference-Isomorphic Graph Families

Many well-studied problems in extremal combinatorics deal with the maximum possible size of a family of objects in which every pair of objects satisfies a given restriction. One problem of this type was recently raised by Alon, Gujgiczer, Körner, Milojević and Simonyi. They asked to determine the maximum size of a family of graphs on [n] such that for every two graphs G and H in the family, the graphs G-H and H-G are isomorphic. We completely resolve this problem by showing that this maximum is exactly 2^{1/2(C(n,2)-[n/2])} and characterizing all the extremal constructions. We also prove an analogous result for r-uniform hypergraphs.

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