In [13], Erd˝os et al. defined the local chromatic number of a graph as the minimum number of colors that must appear within distance 1 of a vertex. For any ∆ ≥ 2, there are ...
Let H be a fixed directed graph on h vertices, let G be a directed graph on n vertices and suppose that at least n2 edges have to be deleted from it to make it H-free. We show tha...