Theorems · Theorem · combinatorics
SimpleGraph.cliqueFree_induce_iff
∀ {α : Type u_1} (G : SimpleGraph α) (s : Set α) (n : ℕ), (SimpleGraph.induce s G).CliqueFree n ↔ G.CliqueFreeOn s n- Defined in
- Mathlib.Combinatorics.SimpleGraph.Clique
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 61 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Finsetproof · cited by 13,712
- SetLike.coeproof · cited by 8,199
- Set.Elemstatement and proof · cited by 7,166
- SimpleGraphstatement and proof · cited by 3,072
- Finset.mapproof · cited by 747
- Function.Embedding.subtypeproof · cited by 128
- SimpleGraph.inducestatement · cited by 80
- SimpleGraph.CliqueFreestatement · cited by 70
- SimpleGraph.IsNCliqueproof · cited by 64
- Finset.subtypeproof · cited by 41
- SimpleGraph.CliqueFreeOnstatement and proof · cited by 11
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