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.