Theorems · Theorem · combinatorics
SimpleGraph.IsNClique.insert
∀ {α : Type u_1} {G : SimpleGraph α} {n : ℕ} {s : Finset α} {a : α} [inst : DecidableEq α],
G.IsNClique n s → (∀ b ∈ s, G.Adj a b) → G.IsNClique (n + 1) (insert a s)- Defined in
- Mathlib.Combinatorics.SimpleGraph.Clique
- Cited by
- 3 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.
Cites12
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
- SetLike.coeproof · cited by 8,199
- SimpleGraphstatement and proof · cited by 3,072
- SimpleGraph.Adjstatement and proof · cited by 1,346
- 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
- SimpleGraph.Adj.neproof · cited by 39
- SimpleGraph.IsNClique.card_eqproof · cited by 17
- SimpleGraph.IsNClique.isCliqueproof · cited by 14
- SimpleGraph.IsClique.insertproof · cited by 1
Cited by3
Results whose statement or proof uses this declaration.
- SimpleGraph.IsNClique.exists_not_adj_of_cliqueFree_succproof · cited by 1
- SimpleGraph.CliqueFreeOn.of_succproof · cited by 0
- SimpleGraph.IsNClique.insert_eraseproof · cited by 0