Henson graph

In graph theory, the Henson graph G_i is an undirected infinite graph, the unique countable homogeneous graph that does not contain an i-vertex clique but that does contain all K_i-free finite graphs as induced subgraphs. For instance, G₃ is a triangle-free graph that contains all finite triangle-free graphs.

These graphs are named after C. Ward Henson, who published a construction for them (for all i ≥ 3) in 1971. The first of these graphs, G₃, is also called the homogeneous triangle-free graph or the universal triangle-free graph.