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arXiv · 1905.08670

Complete Acyclic Colorings

Stefan Felsner·Winfried Hochstättler·Kolja Knauer·Raphael Steiner
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Abstract

We study two parameters that arise from the dichromatic number and the vertex-arboricity in the same way that the achromatic number comes from the chromatic number. The adichromatic number of a digraph is the largest number of colors its vertices can be colored with such that every color induces an acyclic subdigraph but merging any two colors yields a monochromatic directed cycle. Similarly, the a-vertex arboricity of an undirected graph is the largest number of colors that can be used such that every color induces a forest but merging any two yields a monochromatic cycle. We study the relation between these parameters and their behavior with respect to other classical parameters such as degeneracy and most importantly feedback vertex sets.

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Stefan Felsner, Winfried Hochstättler, Kolja Knauer, Raphael Steiner. 2019-05-21. Complete Acyclic Colorings. https://arxiv.org/abs/1905.08670

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