Geodesic
Solution of Irving's Ramsey problem
Glasgow mathematical journal, Tome 21 (1980) no. 2, pp. 187-197

Voir la notice de l'article provenant de la source Cambridge University Press

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+i,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. 
Harborth, Heiko; Nitzschke, Heinz-Michael. Solution of Irving's Ramsey problem. Glasgow mathematical journal, Tome 21 (1980) no. 2, pp. 187-197. doi: 10.1017/S0017089500004353
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[1] 1.Guy, R. K., (Ed.), Sixth British Combinatorial Conference, Unsolved Problems, No. 13 (Typescript 1977). Google Scholar

[2] 2.Harary, F., Graph theory, (Addison-Wesley, 1969). Google Scholar | DOI

[3] 3.Harborth, H. and Mengersen, I., Ein Extremalproblem für Matrizen aus Nullen und Einsen, J. Reine Angew. Math. 309 (1979), 149–155. Google Scholar

[4] 4.Irving, R. W., A bipartite Ramsey problem and the Zarankiewicz numbers. Glasgow Math. J. 19 (1978), 13–26. Google Scholar

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