Square coloring is a variant of graph coloring where vertices within distance two must receive different colors. When considering planar graphs, the most famous conjecture (Wegner, 1977) states that 3 2 ∆ + 1 colors are sufficient to square color every planar graph of maximum degree ∆. This conjecture has been proven asymptotically for graphs with large maximum degree. We consider here planar graphs with small maximum degree and show that 2∆ + 7 colors are sufficient, which improves the best known bounds when 6 ∆ 31.
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