Combinatorics / CONCEPT

Fifteen-vertex separation and the fourteen-vertex bound

Let H be a finite family of subsets of an n-element vertex type. Under DUF, complete blocks with different centers have at most one vertex in each side-intersection cell, and the four cells cannot all be occupied. Under the additional cap of at most four neighbors per ground pair, these blocks are whole link components and satisfy the center and component separation bounds. Three-uniformity is assumed only for the final counting bound.