Abstract :

Property B was introduced by Felix Bernstein in 1906. For each $n$, $m(n)$ is defined to be the largest integer such that each $n$-uniform hypergraph with at most $m(n)$ hyperedges is 2-colorable. Results presenting improvements on the asymptotic bounds of $m(n)$ have been sporadic and exciting. The talk aims to present an exposition of the known bounds on $m(n)$.