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 ...