Theorems · Theorem · combinatorics

SimpleGraph.farFromTriangleFree_iff

∀ {α : Type u_1} {𝕜 : Type u_3} [inst : Field 𝕜] [inst_1 : LinearOrder 𝕜] {G : SimpleGraph α} {ε : 𝕜}
  [inst_2 : Fintype α] [inst_3 : DecidableRel G.Adj],
  G.FarFromTriangleFree ε ↔
    ∀ ⦃H : SimpleGraph α⦄ [inst_4 : DecidableRel H.Adj],
      H ≤ G → H.CliqueFree 3 → ε * ↑(Fintype.card α ^ 2) ≤ ↑G.edgeFinset.card - ↑H.edgeFinset.card

Defined in

Mathlib.Combinatorics.SimpleGraph.Triangle.Basic

Cited by

3 results in Mathlib

Foundations

Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FieldLinearOrderFintypeDecidableRel