Annals of Combinatorics 3 (1999) 53-59

Some Generalizations of Property B and the SplittingProperty

Péter L. Erdös

Institute of Mathematics, Hungarian Academy of Sciences,P.O. Box 127, Budapest, H-1364, Hungary

Received September 16, 1998

AMS Subject Classification: 05D05, 06A07

Abstract.The set system satisfies Property B if there exists a partition X1∪X2=X suchthat any element of H intersects both classes. Here, westudy the following problem: We are given kset systems on the underlying set X, and we are seekinga k-partition of X such that any element of theith set system intersects Xi for every i.

Keywords: Property B, splitting property

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