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A bipartite Ramsey problem and the Zarankiewicz numbers

Published online by Cambridge University Press:  18 May 2009

Robert W. Irving
Robert W. Irving
Affiliation:
Department of Mathematics, University of Salford, Salford M5 4WT
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Beineke and Schwenk [1] have defined the bipartite Ramsey number R(m,n), for integers m, n (1≤m≤n ), to be the smallest integer p such that any 2-colouring of the edges of the complete bipartite graph Kp, v forces the appearance of a monochromatic Km, n. In [1] the following results are established:

with equality if there is a Hadamard matrix of order 2(n−1), n odd,

if there is a Hadamard matrix of order 4(n−1),

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 19 , Issue 1 , January 1978 , pp. 13 - 26
Copyright
Copyright © Glasgow Mathematical Journal Trust 1978

References

REFERENCES

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