2-Distance coloring of planar graph

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The [Formula: see text]-2-distance coloring of graph [Formula: see text] is a mapping [Formula: see text] if any two vertices at distance at most two from each other get different colors. The 2-distance chromatic number is the smallest integer [Formula: see text] such that [Formula: see text] has a [Formula: see text]-[Formula: see text]-distance coloring, denoted by [Formula: see text]. The purpose of this paper is to prove that every planar graph [Formula: see text] without [Formula: see text]-cycle and intersecting [Formula: see text]-cycle and [Formula: see text] has [Formula: see text].