Packing coloring

Summary

In graph theory, a packing coloring (also called a broadcast coloring) is a type of graph coloring where vertices are assigned colors (represented by positive integers) such that the distance between any two vertices with the same color $i$ is greater than $i$. The packing chromatic number (or broadcast chromatic number) $\chi_\rho(G)$ (or $\chi_b(G)$) of a graph $G$ is the minimum number of colors needed for a packing coloring.