A note on the transversal size of a series of families constructed over Cycle Graph

Abstract

Paul Erdős and László Lovász established by means of an example that there exists a maximal intersecting family of $k-$sets with approximately $(e-1)k!$ blocks. László Lovász conjectured that their example is best known example which has the maximum number of blocks. Later it was disproved. But the quest for such examples remain valid till this date. In this short note, by computing transversal size of a certain series of uniform intersecting families constructed over the cycle graph, we provide an example which has more than $(\frac{k}{2}{)}^{k-1}$ (approximately) blocks.

Comments are welcome

References in corpus (1)

• Closed Intersecting Families of finite sets and their applications