2-distance 20-coloring of planar graphs with maximum degree 6

A 2-distance \(k\)-coloring of a graph \(G\) is a proper \(k\)-coloring such that any two vertices at distance two or less get different colors. The 2-distance chromatic number of \(G\) is the minimum \(k\) such that \(G\) has a 2-distance \(k\)-coloring, denoted by \(\chi_2(G)\). In this paper, we show that \(\chi_2(G) \leq 20\) for every planar graph \(G\) with maximum degree at most six, which improves a former bound \(\chi_2(G) \leq 21\).