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arXiv · 2103.11917

The digrundy number of digraphs

Gabriela Araujo-Pardo·Juan José Montellano-Ballesteros·Mika Olsen·Christian Rubio-Montiel
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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.]

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Gabriela Araujo-Pardo, Juan José Montellano-Ballesteros, Mika Olsen, Christian Rubio-Montiel. 2021-03-22. The digrundy number of digraphs. https://arxiv.org/abs/2103.11917

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