Theorems · Theorem · combinatorics
SimpleGraph.not_cliqueFree_iff_top_isContained
∀ {α : Type u_1} {G : SimpleGraph α} (n : ℕ), ¬G.CliqueFree n ↔ (SimpleGraph.completeGraph (Fin n)).IsContained G- Defined in
- Mathlib.Combinatorics.SimpleGraph.Clique
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- SimpleGraphstatement and proof · cited by 3,072
- SimpleGraph.CliqueFreestatement and proof · cited by 70
- SimpleGraph.IsContainedstatement · cited by 68
- SimpleGraph.completeGraphstatement · cited by 49
- SimpleGraph.Embedding.isContainedproof · cited by 4
- SimpleGraph.IsContained.not_cliqueFreeproof · cited by 3
- SimpleGraph.topEmbeddingOfNotCliqueFreeproof · cited by 2
Cited by7
Results whose statement or proof uses this declaration.
- SimpleGraph.cliqueFree_iffproof · cited by 4
- SimpleGraph.CliqueFree.replaceVertexproof · cited by 3
- SimpleGraph.CliqueFree.comapproof · cited by 2
- SimpleGraph.IsContained.not_cliqueFree_cardproof · cited by 1
- SimpleGraph.not_cliqueFree_iffproof · cited by 0
- SimpleGraph.IsAcyclic.cliqueFreeproof · cited by 0
- SimpleGraph.cliqueFree_iff_top_freeproof · cited by 0