Ramsey’s theorem says that for every clique H1 and for every graph H2 with no edges, all graphs containing neither of H1,H2 as induced subgraphs have bounded order. What if, instead, we exclude a graph H1 with a vertex whose deletion gives a clique, and the complement H2 of another such graph? This no longer implies bounded order, but it implies tightly restricted structure that we describe. Th...
