Graph Coloring • 3D Illustration • Math: Graph Theory & Combinatorics

Editorial illustration for a math article at Quanta: "A 53-Year-Old Network Coloring Conjecture Is Disproved" (

At a glance this network doesn't look complicated. You can make a 3D network easily in any software, and there are various plugins to help. But this isn't just any network: it's an example of graph coloring — a mathematical problem where colors (or other labels) are assigned to parts of a graph within specific constraints.

The vertices in this particular 3D graph are allowed to be one of 4 different colors, and no two vertices of the same color can be connected. No green vertex shares an edge with another green, etc. This chromatic number, 4, depends on a network's features, like how many connections each vertex has.