Vol. 80, No. 2, 1979

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

Frank Harary and Robert William Robinson

Vol. 80 (1979), No. 2, 435–441

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 Kp contains a monochromatic G. An isomorphic factorization of Kp 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 Kn 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
Received: 23 May 1978
Published: 1 February 1979
Frank Harary
Robert William Robinson