C(υ, k, 2) denotes the minimum number of k-subsets required to cover all pairs of a υ-set. Obviously, C(n2+ n + 1, n + 1, 2) ≥n2+ n + 1 where equality holds if and only if a finite projective plane exists. In this note the following conjecture of Mendelsohn is proved. If a PG(2, n) does not exist, then C(n2+ n + 1)≥n2+ n + 3.
ASJC Scopus subject areas
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics