Theorems · Theorem · combinatorics
SimpleGraph.CliqueFree.replaceVertex
∀ {α : Type u_1} {G : SimpleGraph α} {n : ℕ} [inst : DecidableEq α],
G.CliqueFree n → ∀ (s t : α), (G.replaceVertex s t).CliqueFree nClique-freeness is preserved by replaceVertex.
- Defined in
- Mathlib.Combinatorics.SimpleGraph.Clique
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 71 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.
Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Set.rangeproof · cited by 4,705
- SimpleGraphstatement and proof · cited by 3,072
- SimpleGraph.Adjproof · cited by 1,346
- Function.Embeddingproof · cited by 988
- SimpleGraph.CliqueFreestatement and proof · cited by 70
- SimpleGraph.completeGraphproof · cited by 49
- SimpleGraph.Embeddingproof · cited by 41
- SimpleGraph.replaceVertexstatement and proof · cited by 15
- Function.Embedding.mk.congr_simpproof · cited by 14
- Function.Embedding.setValueproof · cited by 8
- SimpleGraph.not_cliqueFree_iff_top_isContainedproof · cited by 7
Cited by3
Results whose statement or proof uses this declaration.
- SimpleGraph.IsTuranMaximal.degree_eq_of_not_adjproof · cited by 1
- SimpleGraph.IsTuranMaximal.not_adj_transproof · cited by 1
- SimpleGraph.IsTuranMaximal.isEquipartitionproof · cited by 1