On (1,2 ¹⁴ )-packing coloring of planar graphs with maximum degree at most five

For a sequence of positive integers [Formula: see text] with [Formula: see text], an [Formula: see text]-packing coloring of a graph [Formula: see text] is a partition of [Formula: see text] into subsets [Formula: see text] such that for every two distinct vertices [Formula: see text] and [Formula: see text] in [Formula: see text], the distance between [Formula: see text] and [Formula: see text] is at least [Formula: see text] for [Formula: see text]. Hence, every 2-distance [Formula: see text]-coloring of [Formula: see text] is also a [Formula: see text]-packing coloring of [Formula: see text]. Recently, Deniz proved that every planar graph with maximum degree [Formula: see text] is [Formula: see text]-packing colorable. We focus on the [Formula: see text]-packing coloring of [Formula: see text], and show that every planar graph [Formula: see text] with [Formula: see text] has a [Formula: see text]-packing coloring.