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Discrete Mathematics, Vol. 223 (1-3) (2000) pp. 83-92
© 2000 Elsevier Science B.V. All rights reserved.
PII: S0012-365X(00)00041-8
K2,2-K1,n and K2,n-K2,n bipartite Ramsey numbers
a Department of Philosophy and Centre for Logic and Epistemology, State University of Campinas, C.P. 6133, Campinas, SP, Brazil
b Department of Mathematics, State University of Maringá, Maringá, PR, Brazil
Received 4 February 1999; received in revised form 15 November 1999; accepted 13 December 1999
Abstract
Some bounds for G1-G2 bipartite Ramsey numbers b(G1;G2) are given, which imply that b(K2,2;K1,n)=n+q for the range q2
q+1
nq2, where q is a prime power. Our new construction establishes in particular that b(K2,n;K2,n)=4n3 if 4n3 is a prime power, reinforcing a weaker form of a conjecture due to Beineke and Schwenk. Particular relationships between b(G1;G2) and G1-G2 Ramsey numbers are also determined.
MSC:
05C55 Keywords:
Generalized Ramsey theory; Bipartite Ramsey number; Strongly regular graphs
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