We discuss the maximum size of uniform intersecting families with covering number at least τ. Among others, we construct a large k-uniform intersecting family with covering number k, which provides a counterexample to a conjecture of Lovász. The construction for odd k can be visualized on an annulus, while for even k on a Möbius band.
ASJC Scopus subject areas
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics