Disjointly representing set systems
A family F of sets is s-disjointly representable if there is a family L of disjoint sets each of size s such that every F ∈ F contains some S ∈ L. Let f(r, s) be the minimum size of a family F of r-sets which is not s-disjointly representable. We give upper and lower bounds on f(r, s) which are within a constant factor when s is fixed. © 2003 Elsevier Science (USA). All rights reserved.
Journal of Combinatorial Theory. Series A
Bollobás, B., & Riordan, O. (2003). Disjointly representing set systems. Journal of Combinatorial Theory. Series A, 102 (1), 1-9. https://doi.org/10.1016/S0097-3165(03)00003-7