Vol. 80, No. 2, 1979

Recent Issues
Vol. 307: 1  2
Vol. 306: 1  2
Vol. 305: 1  2
Vol. 304: 1  2
Vol. 303: 1  2
Vol. 302: 1  2
Vol. 301: 1  2
Vol. 300: 1  2
Online Archive
The Journal
Editorial Board
Submission Guidelines
Submission Form
Policies for Authors
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Special Issues
Author Index
To Appear
Other MSP Journals
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