Theorems · Theorem · combinatorics
SimpleGraph.cliqueFree_of_card_lt
∀ {α : Type u_1} {G : SimpleGraph α} {n : ℕ} [inst : Fintype α], Fintype.card α < n → G.CliqueFree nSee SimpleGraph.cliqueFree_of_chromaticNumber_lt for a tighter bound.
- Defined in
- Mathlib.Combinatorics.SimpleGraph.Clique
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Fintype
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Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Fintypestatement and proof · cited by 7,736
- SimpleGraphstatement and proof · cited by 3,072
- Fintype.cardstatement and proof · cited by 1,386
- Nonempty.someproof · cited by 340
- Fintype.card_finproof · cited by 270
- SimpleGraph.CliqueFreestatement · cited by 70
- SimpleGraph.Copyproof · cited by 49
- SimpleGraph.completeGraphproof · cited by 49
- Fintype.card_le_of_embeddingproof · cited by 11
- SimpleGraph.Copy.toEmbeddingproof · cited by 9
- SimpleGraph.cliqueFree_iffproof · cited by 4
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