A set T is said to cover a set system J if T meets all members of J. We raise the following general problem. Find relations among the natural numbers p, r, s, t, that imply the truth of the following statement: If J. is an r-uniform set system such that each of its subsystems on at most p elements can be covered with an s-element set, then J. can be covered with a t-element set. Here we investigate the case s = 1.
ASJC Scopus subject areas
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics