Antidirected subgraphs of oriented graphs

We show that for every η > 0 every sufficiently large n -vertex oriented graph D of minimum semidegree exceeding (1+η ) k2 contains every balanced antidirected tree with k edges and bounded maximum degree, if k≥ η n . 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 .