Dear all,
There will be a noon seminar this Thursday, 23 October, given by Marek Skrzypczyk. Please find the talk details below.
Best regards, Misha Tyomkyn.
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Antidirected paths in oriented graphs Marek Skrzypczyk Jagiellonian University
October 23, 2025, 12:20 in S6 Abstract
An antidirected path is an orientation of a path such that for each vertex v we have either d^-(v)=0 or d^+(v)=0. In this talk I will show that for any integer k > 3, every oriented graph with minimum semidegree bigger than k/2+\sqrt{k}/2 contains an antidirected path of length k. Consequently, every oriented graph on n vertices with more than (k+\sqrt{k})n edges contains an antidirected path of length k. This asymptotically proves the antidirected path version of a conjecture of Stein and of a conjecture of Addario-Berry, Havet, Linhares Sales, Reed and Thomassé, respectively.
This is joint work with Andrzej Grzesik
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