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 ...

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 ...

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 ...

Consider a finite nonnull graph $G$ with no loops or multiple edges and no isolated points. Its Ramsey number $r(G)$ is defined as the minimum number $p$ such that ...

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 ...