Zentralblatt MATH

Publications of (and about) Paul Erdös

Zbl.No:  249.05003
Autor:  Erdös, Paul; O'Neil, Patrik E.
Title:  On a generalization of Ramsey numbers. (In English)
Source:  Discrete Math. 4, 29-35 (1973).
Review:  Define m = N(l1,k1; l2,k2; r) as the smallest integer with the property that if the r-tuples of a set of m elements are arbitrarily split into two classes then for i = 1 or 2 there exists a subset of size li each of whose subsets of size ki lies in some r-subset of the i-th class. N(l1,r; l2; r; r) is the Ramsey number N(l1,l2; r). The authors prove that if k1+k2 = r+1 then

N(l1,k1; l2,k2; r) = l1+l2-k1-k2+1.

If k+1+k2 = r+2 the authors prove

2c1l < N(l1,k1; l2,k2; r) < 2c2l.

Classif.:  * 05A05 Combinatorial choice problems

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