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Theorems · Theorem · combinatorics

SimpleGraph.is3Clique_iff

∀ {α : Type u_1} {G : SimpleGraph α} {s : Finset α} [inst : DecidableEq α],
  G.IsNClique 3 s ↔ ∃ a b c, G.Adj a b ∧ G.Adj a c ∧ G.Adj b c ∧ s = {a, b, c}
Defined in
Mathlib.Combinatorics.SimpleGraph.Clique
Cited by
1 results in Mathlib
Foundations
Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
DecidableEq
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

SimpleGraph.TripartiteFromTriangles.is3Clique_iff · cited by 2TripartiteFromTriangles.i…Finset · cited by 13712FinsetSimpleGraph · cited by 3072SimpleGraphSimpleGraph.Adj · cited by 1346SimpleGraph.AdjSimpleGraph.IsNClique · cited by 64SimpleGraph.IsNCliqueSimpleGraph.IsNClique.card_eq · cited by 17IsNClique.card_eqFinset.card_eq_three · cited by 4Finset.card_eq_threeSimpleGraph.is3Clique_triple_iff · cited by 2SimpleGraph.is3Clique_tri…SimpleGraph.is3Clique_iffCITED BYCITES

Cites7

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Cited by1

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