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Monochromatic triangles in three colours

Published online by Cambridge University Press:  17 April 2009

S.S. Sane  and
W.D. Wallis
S.S. Sane
Affiliation:
Center of Advanced Study in Mathematics, University of Bombay, Bombay 400 098, India
W.D. Wallis
Affiliation:
Department of Computer Science, and Department of Mathematics, Southern Illinois University at Carbondale, Carbondale, Illinois 62901, United States of America
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Abstract

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Suppose the edges of the complete graph on 17 vertices are coloured in three colours. It is shown that at least five monochromatic triangles must aris.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 37 , Issue 2 , April 1988 , pp. 197 - 212
Copyright
Copyright © Australian Mathematical Society 1988

References

[1]Goodman, A.W., ‘On Sets of acquaintances and strangers at any party’, Amer. Math. Monthly 66 (1959), 778–783.CrossRefGoogle Scholar
[2]Goodman, A.W., ‘Triangles in a complete chromatic graph with three colors’, Discrete Math. 57 (1985), 225–235.CrossRefGoogle Scholar
[3]Greenwood, R. E. and Gleason, A. M., ‘Combinatorial relations and chromatic graphs’, Canad. J. Math. 7 (1955), 1–7.CrossRefGoogle Scholar
[4]Harary, F., ‘The two-triangle case of the acquaintance graph’, Math. Mag. 45 (1972), 130–135.CrossRefGoogle Scholar
[5]Harary, F. and Prins, G., ‘Generalized Ramsey theory for graphs IV: The Ramsey multiplicity of a graph’, Networks 4 (1974), 163–173.CrossRefGoogle Scholar
[6]Wallis, W.D., ‘The number of monochromatic triangles in edge-colourings of a complete graph’, J. Combin. Inform. System. Sci. 1 (1976), 17–20.Google Scholar
[7]Wallis, W.D., Street, A.P. and Wallis, J.S., Combinatorics: Room Squares, Sum-free Sets, Hadamard Matrices, Lecture Notes in Math. 292 (Springer-Verlag, Heidelberg, 1972).CrossRefGoogle Scholar