Geodesic
Complete acyclic colorings
The electronic journal of combinatorics, Tome 27 (2020) no. 2

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Zbl DOI arXiv
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.
DOI : 10.37236/8752
Classification : 05C15, 05C20
Mots-clés : adichromatic number of a digraph 
Stefan Felsner; Winfried Hochstättler; Kolja Knauer; Raphael Steiner. Complete acyclic colorings. The electronic journal of combinatorics, Tome 27 (2020) no. 2. doi: 10.37236/8752
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     title = {Complete acyclic colorings},
     journal = {The electronic journal of combinatorics},
     year = {2020},
     volume = {27},
     number = {2},
     doi = {10.37236/8752},
     zbl = {1441.05073},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/8752/}
}
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