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

Frank Harary and Robert William Robinson

Vol. 80 (1979), No. 2, 435–441

DOI: 10.2140/pjm.1979.80.435

Abstract

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.

Mathematical Subject Classification 2000

Primary: 05C55

Milestones

Received: 23 May 1978

Published: 1 February 1979