Theorems · Theorem · combinatorics

SimpleGraph.CliqueFree.not_farFromTriangleFree

∀ {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],
  G.CliqueFree 3 → 0 < ε → ¬G.FarFromTriangleFree ε

Defined in: Mathlib.Combinatorics.SimpleGraph.Triangle.Basic
Cited by: 0 results in Mathlib
Foundations: Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Field LinearOrder IsStrictOrderedRing Fintype DecidableRel Nonempty

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LinearOrderstatement and proof · cited by 8,572
Fintypestatement and proof · cited by 7,736
Fieldstatement and proof · cited by 7,404
SimpleGraphstatement and proof · cited by 3,072
IsStrictOrderedRingstatement and proof · cited by 2,490
SimpleGraph.Adjstatement and proof · cited by 1,346
LE.le.not_gtproof · cited by 189
SimpleGraph.CliqueFreestatement and proof · cited by 70
SimpleGraph.FarFromTriangleFreestatement and proof · cited by 15
SimpleGraph.FarFromTriangleFree.nonposproof · cited by 2

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