Algorithmic Quasirandom Lemma Sample Clauses

Algorithmic Quasirandom Lemma. For all γ, δ > 0 and functions ε : (0, 1] → (0, 1] there exist positive integers P0 and N0 so that the following holds. For every 3-uniform hypergraph H on vertex set V = V (H), where |V | = N > N0, one can construct in time O(N 6): (i) a vertex partition V = V1 ∪ · · · ∪ Vt with |V1| ≤ · · · ≤ |Vt| ≤ |V1| + 1, and (ii) a pair-partition of V given by, for each 1 ≤ i < j ≤ t, K[Vi, Vj] = lij 1≤i <j≤t Gij ∪ · · · ∪ Gij , with a total number of parts Σ lij ≤ P0 and All but ▇▇ ▇ ▇▇▇▇▇▇▇ {▇▇, ▇▇, vk} ∈ V satisfy that whenever {vi, vj, vk} ∈ 3