Generalized Ramsey theory. IX. Isomorphic factorizations. IV. Isomorphic Ramsey numbers.

The ramsey number of a graph G with no isolates has been defined as the minimum p such that every 2-coloring of (the lines of) the complete graph K p contains a monochromatic G. An isomorphic factorization of K p is a partition of its lines into isomorphic subgraphs. Combining these concepts, we define the isomorphic ramsey number of G as the minimum p such that for all n^p, every 2-coloring of K n which induces an isomorphic factorization contains a monochromatic G. The isomorphic ramsey numbers of all the small graphs (with at most four points) are determined. The extension to c > 2 colors is also studied.