Combinatorics / CONCEPT

Ownership at a marked exchange

Let V be any finite vertex type and H any finite family of its subsets. Write N_H(p) for the vertices x outside p with insert(x,p) in H, and K_H(q) for the two-element ground sets p with q contained in N_H(p). An exact marked exchange determines the packet and row of either endpoint. No uniformity, disjoint-union uniqueness, or codegree cap is required for this local assertion.