A new algorithm efficiently solves the graph isomorphism problem, which has puzzled computer scientists for decades.

De Grey pitched the problem of finding the minimal five-color graph to Terence Tao, a mathematician at the University of California, Los Angeles, as a potential Polymath problem.

Graph Coloring: The process of assigning colours to vertices or edges of a graph so that adjacent elements have distinct colours, commonly used in scheduling and resource allocation problems.

Distributed algorithms for graph problems represent a vibrant area of study that addresses the challenges of decentralised computation across interconnected networks.

But that doesn't mean five is the absolute minimum. Mathematicians know that it's possible that a graph will come along requiring six colors of paint, or even seven.

Graph coloring has been employed since the 1980s to efficiently compute sparse Jacobian and Hessian matrices using either finite differences or automatic differentiation. Several coloring problems ...