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 ...

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 ...

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 ...

Bulletin mathématique de la Société des Sciences Mathématiques de Roumanie, Nouvelle Série, Vol. 51 (99), No. 3 (2008), pp. 177-182 (6 pages) For given graphs G and H, the Ramsey number R(G, H) is the ...

Generally when assuming a chaotic (i.e. random) system like an undirected graph, we assume that if we start coloring these (i.e. assign values) with two colors no real pattern emerges. Yet it’s been ...

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 ...