Theorems · Theorem · combinatorics
SimpleGraph.IsNClique.insert_erase
∀ {α : Type u_1} {G : SimpleGraph α} {n : ℕ} {s : Finset α} {a b : α} [inst : DecidableEq α],
G.IsNClique n s → (∀ w ∈ s \ {b}, G.Adj a w) → b ∈ s → G.IsNClique n (insert a (s.erase b))- Defined in
- Mathlib.Combinatorics.SimpleGraph.Clique
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 62 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.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement and proof · cited by 13,712
- SimpleGraphstatement and proof · cited by 3,072
- SimpleGraph.Adjstatement and proof · cited by 1,346
- Finset.erasestatement and proof · cited by 455
- SimpleGraph.IsNCliquestatement and proof · cited by 64
- Finset.notMem_emptyproof · cited by 40
- SimpleGraph.IsNClique.insertproof · cited by 3
- SimpleGraph.IsNClique.erase_of_memproof · cited by 1
- SimpleGraph.isNClique_zeroproof · cited by 1
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.