2-Distance coloring of planar graphs without adjacent 5-cycles

The k-2-distance coloring of graph G is a mapping c : V (G) ? {1, 2, ... , k} such that any two vertices at distance at most two from each other get different colors. The 2-distance chromatic number is the smallest integer k such that G has a k-2-distance coloring, denoted by ?(2)(G). In this paper, we prove that every planar graph G without adjacent 5-cycles and g(G) = 5 and ?(G) = 17 has ?(2)(G) = ? + 3.

Automated summary

In this paper, it is proved that for a planar graph G without adjacent 5-cycles and g(G) = 5 and ?(G) = 17, the 2-distance chromatic number is ? + 3.