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Solution of Irving's Ramsey problem
Published online by Cambridge University Press: 18 May 2009
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In [1] the following question was posed by R. W. Irving (see also Conjecture 4.10 in [4]): Is there an edge 2-colouring of the complete bipartite graph K13,17 with no monochromatic K3,3? We give a negative answer in this note (Theorem 2). Furthermore we prove Conjecture 4.11 (i) of [4] (Theorem 1), that is, any edge 2-coloured K2n+1,4n−3 contains a monochromatic K2,n with the 2 and n vertices a subset of the 2n+1 and 4n−3 vertices, respectively. Theorem 1 is a consequence of Satz 4 in [3], however, we give a direct proof here.
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- Copyright © Glasgow Mathematical Journal Trust 1980
References
REFERENCES
1.Guy, R. K., (Ed.), Sixth British Combinatorial Conference, Unsolved Problems, No. 13 (Typescript 1977).Google Scholar
3.Harborth, H. and Mengersen, I., Ein Extremalproblem fur Matrizen aus Nullen und Einsen, J. Reine Angew. Math. 309 (1979), 149–155.Google Scholar
4.Irving, R. W., A bipartite Ramsey problem and the Zarankiewicz numbers. Glasgow Math. J. 19 (1978), 13–26.CrossRefGoogle Scholar
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