Graphs with maximum degree 5 are acyclically 7-colorable - Kostochka, Alexandr V. (Ars mathematica contemporanea, 2011)
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 ?$\left( 1 + \lfloor \frac{(r + 1)^2}{4} \rfloor \right)$?-coloring.
Keywords: aciklično barvanje; acyclic coloring; graph theory; maksimalna stopnja; maximum degree; teorija grafov