Design for Clause Samples

Design for n = (3t − k) Definition 6 (Edge Graph). Given a 3-uniform hypergraph H(P, E), the edge graph of a node v ∈ P is defined as Gv(Pv, Ev) where Pv = P − {v} and Ev = {{i, j}|{i, j, v}∈ E}. on E whenever (i − j) mod (n − 1) ≤ t+k . Clearly G(V, E) is (t + k)-connected. For constructing a (3,t)-hyper-(3t − n + 1)-connected hypergraph H(P, E) n = (3t − k) nodes, we consider P× = {v0, v1, v2,..., vk} ⊂ P and place 3- hyperedges such that for each i, 0 ≤ i ≤ k, vi’s edge graph is (t + k)-connected. The edge graph is isomorphic to G(V,, E),where V = {1, 2,...,n−1} and {i, j}∈ Claim. H(P, E) is (3,t)-hyper-(3t − n + 1)-connected.