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Proper colourings of K15

Published online by Cambridge University Press:  09 April 2009

Katherine Heinrich
Katherine Heinrich
Affiliation:
University of Newcastle, Newcastle, N.S.W. 2308, Australia.
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Abstract

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We denote the complete graph on n vertices by Kn. A proper k–colouring of Kn is a way of assigning colours from a set of k colours to the edges of Kn in such a way that no monochromatic triangles are formed. It is known that there are precisely two proper 3-colourings of K16 each of which has exactly one proper 3-colouring of K15 embedded in it. We show that these two are the only proper 3-colourings of K15.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 24 , Issue 4 , December 1977 , pp. 465 - 495
Copyright
Copyright © Australian Mathematical Society 1977

References

Kalbfleisch, J. G. and Stanton, R. G. (1968), “On the maximal triangle-free edge chromatic graphs in three colours”, J. Combinatorial Theory 5, 9–20.CrossRefGoogle Scholar
Street, Anne Penfold and Wallis, W. D. (1976), “Sum-free sets, coloured graphs and designs”, J. Austral. Math. Soc. (Ser A) 22, 35–53.CrossRefGoogle Scholar
Wallis, W. D., Street, Anne Penfold and Wallis, Jennifer Seberry (1972), Combinatorics: Room Squares, Sum-Free Sets, Hadamard Matrices. Lecture Notes in Mathematics 292, (Springer-Verlag).CrossRefGoogle Scholar