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

Date and Time: Thursday, September 30, 2021, 12:15 pm

Duration: 30 minutes

Location: CAB G51 and Zoom: conference room

Speaker: Oliver Janzer

Counting H-free orientations of graphs

In 1974, Erdős posed the following problem. Given an oriented graph H, determine or estimate the maximum possible number of H-free orientations of an n-vertex graph. When H is a tournament, the answer was determined precisely for sufficiently large n by Alon and Yuster. In general, when the underlying undirected graph of H contains a cycle, one can obtain accurate bounds by combining an observation of Kozma and Moran with celebrated results on the number of F-free graphs. We resolve all remaining cases in an asymptotic sense, thereby giving a rather complete answer to Erdős's question. Moreover, we determine the answer exactly when H is an odd cycle and n is sufficiently large, answering a question of Araújo, Botler and Mota. Joint work with Matija Bucic and Benny Sudakov.

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