We show that for any integer $k \ge 4$, every oriented graph with minimum semidegree bigger than $\frac{ 1}{ 2}(k-1+\sqrt{ k-3})$ contains an antidirected path of length $k$. Consequently, every oriented graph on $n$ vertices with more than $(k-1+\sqrt{ k-3})n$ 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 Thomass\'e, respectively.
Categories: math.CO