Acyclic sets and colorings in digraphs under restrictions on degrees and cycle lengths

Ararat Harutyunyan, Colin McDiarmid, Gil Puig i Surroca

Given a digraph $D$, we denote by $\vec{\hat{I}}\pm (D)$ the maximum size of an acyclic set of $D$ (i.e. a set of vertices which induces a subdigraph with no directed cycles), and by $\vecχ(…