Theorems · Theorem · combinatorics
SimpleGraph.is3Clique_triple_iff
∀ {α : Type u_1} {G : SimpleGraph α} {a b c : α} [inst : DecidableEq α],
G.IsNClique 3 {a, b, c} ↔ G.Adj a b ∧ G.Adj a c ∧ G.Adj b c- Defined in
- Mathlib.Combinatorics.SimpleGraph.Clique
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 61 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DecidableEq
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement · cited by 13,712
- SimpleGraphstatement and proof · cited by 3,072
- SimpleGraph.Adjstatement and proof · cited by 1,346
- Finset.coe_singletonproof · cited by 145
- Finset.card_singletonproof · cited by 144
- Finset.coe_insertproof · cited by 124
- SimpleGraph.IsCliqueproof · cited by 76
- SimpleGraph.IsNCliquestatement and proof · cited by 64
- Finset.card_insert_of_notMemproof · cited by 45
- Finset.insert_eq_of_memproof · cited by 28
Cited by2
Results whose statement or proof uses this declaration.
- SimpleGraph.is3Clique_iffproof · cited by 1
- SimpleGraph.isIndepSet_neighborSet_of_triangleFreeproof · cited by 0