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Pré-Publication, Document De Travail Année : 2020

Complete Acyclic Colorings

Résumé

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.

Dates et versions

hal-02436193 , version 1 (12-01-2020)

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Stefan Felsner, Winfried Hochstättler, Kolja Knauer, Raphael Steiner. Complete Acyclic Colorings. 2020. ⟨hal-02436193⟩
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