Combinatorics / CONCEPT

Charging saturated link components

Let V be a finite vertex type and H a finite family of subsets of V. The DUF condition says that an unordered pair of disjoint members of H is uniquely determined by its union. Write N(p) for the vertices outside p that extend p to a member of H, and K(q) for the family of ground pairs p with q contained in N(p). The cap-four hypothesis requires card(N(p))<=4 for every ground pair p, including absent pairs.