Abstract

We show that for every η > 0 every sufficiently large n-vertex oriented graph D of minimum semidegree exceeding (1 + η) 2k contains every balanced antidirected tree with k edges and bounded maximum degree, if k ≥ ηn. In particular, this asymptotically confirms a conjecture of the first author for long antidirected paths and dense digraphs. Further, we show that in the same setting, D contains every k-edge antidirected subdivision of a sufficiently small complete graph, if the paths of the subdivision that have length 1 or 2 span a forest. As a special case, we can find all antidirected cycles of length at most k. Finally, we address a conjecture of Addario-Berry, Havet, Linhares Sales, Reed, and Thomassé for antidirected trees in digraphs. We show that this conjecture is asymptotically true in n-vertex oriented graphs for all balanced antidirected trees of bounded maximum degree and of size linear in n.