The transversal number τ(H) of a hypergraph H is the minimum cardinality of a set of vertices that intersects all edges of H. For k ≥ 1 define ck =sup τ(H)/(m + n), where H ranges over all k-uniform hypergraphs with n vertices and m edges. Applying probabilistic arguments we show that ck = (1 +o(1))logek/k. This settles a problem of Tuza.
All Science Journal Classification (ASJC) codes
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics