Theorems · Theorem · combinatorics
SimpleGraph.IsNClique.erase_of_sup_edge_of_mem
∀ {α : Type u_1} {G : SimpleGraph α} [inst : DecidableEq α] {v w : α} {s : Finset α} {n : ℕ},
(G ⊔ SimpleGraph.edge v w).IsNClique n s → v ∈ s → G.IsNClique (n - 1) (s.erase v)- Defined in
- Mathlib.Combinatorics.SimpleGraph.Clique
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 57 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 and proof · cited by 13,712
- SimpleGraphstatement and proof · cited by 3,072
- Finset.erasestatement · cited by 455
- SimpleGraph.IsNCliquestatement and proof · cited by 64
- SimpleGraph.edgestatement and proof · cited by 44
- Finset.card_erase_of_memproof · cited by 38
- SimpleGraph.IsNClique.card_eqproof · cited by 17
- Finset.coe_eraseproof · cited by 17
- SimpleGraph.IsNClique.isCliqueproof · cited by 14
- SimpleGraph.IsClique.sdiff_of_sup_edgeproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- SimpleGraph.CliqueFree.sup_edgeproof · cited by 2
- SimpleGraph.exists_of_maximal_cliqueFree_not_adjproof · cited by 1