Solution of Irving's Ramsey problem

Solution of Irving's Ramsey problem

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),...

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Veröffentlicht in:Glasgow mathematical journal 1980-01, Vol.21 (1), p.187-197
Hauptverfasser: Harborth, Heiko, Nitzschke, Heinz-Michael
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description 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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