Theorems · Theorem · combinatorics

SimpleGraph.FarFromTriangleFree.cliqueFinset_nonempty

∀ {α : Type u_1} {𝕜 : Type u_3} [inst : Field 𝕜] [inst_1 : LinearOrder 𝕜] [IsStrictOrderedRing 𝕜] {G : SimpleGraph α}
  {ε : 𝕜} [inst_3 : Fintype α] [inst_4 : DecidableRel G.Adj] [Nonempty α] [inst_6 : DecidableEq α],
  G.FarFromTriangleFree ε → 0 < ε → (G.cliqueFinset 3).Nonempty

Defined in

Mathlib.Combinatorics.SimpleGraph.Triangle.Basic

Cited by

1 results in Mathlib

Foundations

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

Assumes

FieldLinearOrderIsStrictOrderedRingFintypeDecidableRelNonemptyDecidableEq