Abstract
The set system\({\cal H} \subseteq 2^X\) satisfiesProperty B if there exists a partitionX 1∪X 2=X such that any element of\({\cal H}\) intersects both classes. Here, we study the following problem: We are givenk set systems on the underlying setX, and we are seeking ak-partition ofX such that any element of theith set system intersectsX i for everyi.
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The paper received its final form when the author enjoyed the hospitality of L.A. Székely of the University of South Carolina, Columbia, South Carolina, USA. The research was partially supported by the Hungarian Scientific Fund, Grant no. T16358.
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Erdős, P.L. Some generalizations of Property B and the splitting property. Annals of Combinatorics 3, 53–59 (1999). https://doi.org/10.1007/BF01609875
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DOI: https://doi.org/10.1007/BF01609875