Anti-Ramsey theory in graphs is a branch of combinatorial mathematics that examines the conditions under which a graph, when its edges are coloured, must necessarily contain a ‘rainbow’ subgraph – a ...

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 ...

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.