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