KERNELS IN DIRECTED-GRAPHS - A POISON GAME

We consider a two player game on a progressively and locally finite di rected graph and we prove that the first player wins if and only if th e graph has a local kernel. The result is sharp. From it, we derive a short proof of a general version of the Galeana-Sanchez & Neuman-Lara Theorem that give a sufficient condition for a digraph to be kernel-pe rfect.