2-Distance Coloring of Planar Graphs with Specific Maximum Degree

Abstract

A k-distance r-coloring of a graph is a coloring of the vertices of the graph such that if the distance between 2 vertices x and y is less or equal to k, then x and y must have distinct colors. A planar graph is a graph that can be drawn with no edge crossing. We will study the 2-distance coloring of planar graphs with maximum degree at least 6.