The digrundy number of digraphs
Combinatorics
2021-03-23 v1
Abstract
We extend the Grundy number and the ochromatic number, parameters on graph colorings, to digraph colorings, we call them {\emph{digrundy number}} and {\emph{diochromatic number}}, respectively. First, we prove that for every digraph the diochromatic number equals the digrundy number (as it happen 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 [Electron. J. Combin. 25 (2018) no. 3, Paper {\#} 3.51, 17 pp.]
Cite
@article{arxiv.2103.11917,
title = {The digrundy number of digraphs},
author = {Gabriela Araujo-Pardo and Juan José Montellano-Ballesteros and Mika Olsen and Christian Rubio-Montiel},
journal= {arXiv preprint arXiv:2103.11917},
year = {2021}
}
Comments
9 pages, 1 figure