Georgia Institute of Technology College of Sciences

Ramsey proved that for every positive integer r, every sufficiently large graph contains as an induced subgraph either a complete graph on r vertices or an independent set with r vertices.  It is well known that every sufficiently large, connected graph contains an induced subgraph isomorphic to one of a large complete graph, a large star, and a long path.  We prove an analogous result for 2-connected graphs.  Similarly, for infinite graphs, every infinite connected graph contains an induced subgraph isomorphic to one of the following: an infinite complete graph, an infinite star, and a ray.  We also prove an analogous result for infinite 2-connected graphs.