Number of lines in hypergraphs
Pierre Aboulker, Adrian Bondy, Chen, Xiaomin, Ehsan Chiniforooshan, Chvátal, Vašek, Peihan Miao · arXiv (Cornell University) · 2013
Chen and Chvátal introduced the notion of lines in hypergraphs; they proved that every 3-uniform hypergraph with $n$ vertices either has a line that consists of all $n$ vertices or else has at least $\log_2 n$ distinct lines. We improve this lower bound by a factor of $2-o(1)$.