Publications of (and about) Paul Erdös
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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