In 1950 Edward Nelson, then a student at the University of Chicago, asked the kind of deceptively simple question that can give mathematicians fits for decades. Imagine, he said, a graph—a collection ...

David Conlon and Asaf Ferber have raised the lower bound for multicolor “Ramsey numbers,” which quantify how big graphs can get before patterns inevitably emerge. “There is no absolute randomness in ...

Vertices and edges of the same color and shape in a graph are mapped to each other by a symmetry permutation preserving the structure of data. News organizations may use or redistribute this image, ...