Geodesic
Graphs with maximum degree 5 are acyclically 7-colorable
Ars Mathematica Contemporanea, Tome 4 (2011) no. 1, pp. 153-164.

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An acyclic coloring is a proper coloring with the additional property that the union of any two color classes induces a forest. We show that every graph with maximum degree at most 5 has an acyclic 7-coloring. We also show that every graph with maximum degree at most r has an acyclic (1 + ⌊(r + 1)2/4⌋-coloring.
DOI : 10.26493/1855-3974.198.541
Keywords: Acyclic coloring, maximum degree 
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Alexandr V. Kostochka; Christopher J. Stocker. Graphs with maximum degree 5 are acyclically 7-colorable. Ars Mathematica Contemporanea, Tome 4 (2011) no. 1, pp. 153-164. doi : 10.26493/1855-3974.198.541. http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.198.541/

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