An overlap representation is an assignment of sets to the vertices of a graph in such a way that two vertices are adjacent if and only if the sets assigned to them overlap. The ov...
The overlap number of a finite (d + 1)-uniform hypergraph H is the largest constant c(H) (0, 1] such that no matter how we map the vertices of H into Rd , there is a point covered...
Jacob Fox, Mikhail Gromov, Vincent Lafforgue, Assa...