Theorems · Theorem · combinatorics
SimpleGraph.CliqueFree.sup_edge
∀ {α : Type u_1} {G : SimpleGraph α} {n : ℕ},
G.CliqueFree n → ∀ (v w : α), (G ⊔ SimpleGraph.edge v w).CliqueFree (n + 1)Adding an edge increases the clique number by at most one.
- Defined in
- Mathlib.Combinatorics.SimpleGraph.Clique
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- Finsetproof · cited by 13,712
- SimpleGraphstatement and proof · cited by 3,072
- SimpleGraph.CliqueFreestatement and proof · cited by 70
- SimpleGraph.IsNCliqueproof · cited by 64
- SimpleGraph.edgestatement and proof · cited by 44
- SimpleGraph.IsNClique.not_cliqueFreeproof · cited by 4
- SimpleGraph.CliqueFree.monoproof · cited by 4
- SimpleGraph.IsNClique.erase_of_sup_edge_of_memproof · cited by 2
- SimpleGraph.CliqueFree.mem_of_sup_edge_isNCliqueproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- SimpleGraph.IsTuranMaximal.card_partsproof · cited by 1
- SimpleGraph.not_cliqueFree_of_isTuranMaximalproof · cited by 0