Gallai–Ramsey theory lies at the intersection of graph colouring and Ramsey theory, providing a framework for understanding how structures emerge in edge-coloured graphs. Central to this domain is the ...

Mathematicians have iterated a new upper-bound limit on a famously elusive math concept: the Ramsey Number. The Ramsey number’s upper bound hasn’t changed since Paul Erdős calculated it in 1935. The ...

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 ...