The digrundy number of digraphs

Abstract

We extend the Grundy number and the ochromatic number, parameters on graph colorings, to digraph colorings, we call them digrundy number and diochromatic number , respectively. First, we prove that for every digraph the diochromatic number equals the digrundy number (as happens for graphs). Then, we prove the interpolation property and the Nordhaus–Gaddum relations for the digrundy number, and improve the Nordhaus–Gaddum relations for the dichromatic and diachromatic numbers bounded previously by the authors in Araujo-Pardo et al. (2018).