Theorems · Theorem · combinatorics

Finpartition.IsEquipartition.card_interedges_sparsePairs_le

∀ {α : Type u_1} {𝕜 : Type u_2} [inst : Field 𝕜] [inst_1 : LinearOrder 𝕜] [IsStrictOrderedRing 𝕜]
  [inst_3 : DecidableEq α] {A : Finset α} {P : Finpartition A} {G : SimpleGraph α} [inst_4 : DecidableRel G.Adj]
  {ε : 𝕜},
  P.IsEquipartition →
    0 ≤ ε →
      ↑((P.sparsePairs G ε).biUnion fun x =>
              match x with
              | (U, V) => G.interedges U V).card ≤
        4 * ε * ↑A.card ^ 2

Defined in

Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform

Cited by

1 results in Mathlib

Foundations

Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FieldLinearOrderIsStrictOrderedRingDecidableEqDecidableRel