Fifty years ago, Paul Erdős and two other mathematicians came up with a graph theory problem that they thought they might solve on the spot. A team of mathematicians has finally settled it. In the ...

Edge colouring is a fundamental concept in graph theory whereby colours are assigned to the edges of a graph such that no two adjacent edges share the same colour. This process is central to numerous ...

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 ...