A visual representation of Ramsey theorem for five nodes on a graph. Here, no triangle has edges that are all the same color, indicating no groups of three that are either all 'friends' or all ...

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 ...

The original version of this story appeared in Quanta Magazine. So far this year, Quanta has chronicled three major advances in Ramsey theory, the study of how to avoid creating mathematical patterns.

The so-called differential equation method in probabilistic combinatorics presented by Patrick Bennett, Ph.D., Department of Mathematics, Western Michigan University Abstract: Differential equations ...