Semidegree conditions for antitrees


We would like to know for which function f(k) it is true that any oriented graph of minimum semidegree at least f(k) necessarily contains a given oriented path with k edges. For the directed path, f(k)=k/2 works, and perhaps this is true for other orientations as well. We show that this is approximately the case for large antidirected paths, and more generally, for large antidirected trees of bounded maximum degree. This is joint work with Camila Zárate.