Mittagsseminar (in cooperation with J. Lengler, A. Steger, and D. Steurer)

Date and Time: Tuesday, October 21, 2025, 12:15 pm

Duration: 30 minutes

Location: CAB G51

Speaker: Patryk Morawski

Ramsey numbers of digraphs with local edge structure

One of the classical topics in graph Ramsey theory is the study of which $n$-vertex graphs have Ramsey numbers that are linear in $n$. In this paper, we consider this problem in the context of directed graphs. The oriented Ramsey number of a digraph $G$ is the smallest integer $N$ such that every $N$-vertex tournament contains a copy of $G$. We prove that every bounded-degree acyclic digraph with a ``local edge structure'' has a linear oriented Ramsey number. This provides a common generalization of several prior results, including on digraphs of bounded height, of digraphs of bounded bandwidth, and blowups of bounded-degree oriented trees. Joint work with Domagoj Bradač, Benny Sudakov and Yuval Wigderson.

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