In 1930, Frank Ramsey proved that if a graph is big enough, it becomes impossible to avoid creating what mathematicians call a monochromatic clique — a group of nodes whose common edges are either all ...

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 ...

Yet it’s been proven that if you have a graph with a certain set of vertices, coloring the resulting lines in this manner will always result in a clique forming. This phenomenon has been ...

What’s more, graph theory lends itself nicely to the development of questions of real mathematical substance. My simple demonstration of the presence of a three-person clique or anti-clique in ...