On the minimum size of 4-uniform hypergraphs without property BB

A hypergraph is said to have property BB if it is 2-colorable. Let m(k)m(k) denote the minimum number of edges in a kk-uniform hypergraph that does not have property BB. Erdős and Hajnal introduced the problem of determining m(k)m(k) in the early 1960s. The smallest cases, m(2)=3m(2)=3 and m(3)=7m(3)=7, are rather straightforward, but the next case has so far withstood all attacks; the possible values have been narrowed down to 21≤m(4)≤2321≤m(4)≤23. By an exhaustive computer search, it is here shown that m(4)=23m(4)=23.