Theorems · Definition · combinatorics
SimpleGraph.topEmbeddingOfNotCliqueFree
{α : Type u_1} → {G : SimpleGraph α} → {n : ℕ} → ¬G.CliqueFree n → SimpleGraph.completeGraph (Fin n) ↪g GAn embedding of a complete graph that witnesses the fact that the graph is not clique-free.
- Defined in
- Mathlib.Combinatorics.SimpleGraph.Clique
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 65 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- SetLike.coeproof · cited by 8,199
- Equiv.symmproof · cited by 3,681
- SimpleGraphstatement and proof · cited by 3,072
- Equiv.toEmbeddingproof · cited by 254
- SimpleGraph.CliqueFreestatement and proof · cited by 70
- SimpleGraph.completeGraphstatement · cited by 49
- SimpleGraph.Embeddingstatement · cited by 41
- SimpleGraph.Embedding.compproof · cited by 10
- SimpleGraph.Embedding.completeGraphproof · cited by 9
- Finset.equivFinOfCardEqproof · cited by 6
- SimpleGraph.Embedding.induceproof · cited by 6
Cited by2
Results whose statement or proof uses this declaration.
- SimpleGraph.not_cliqueFree_iff_top_isContainedproof · cited by 7
- SimpleGraph.CliqueFree.replaceVertexproof · cited by 3