Theorems · Theorem · combinatorics
SimpleGraph.cliqueFree_completeMultipartiteGraph
∀ {n : ℕ} {ι : Type u_3} [inst : Fintype ι] (V : ι → Type u_4),
Fintype.card ι < n → (SimpleGraph.completeMultipartiteGraph V).CliqueFree nA complete r-partite graph has no n-cliques for r < n.
- 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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Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Fintypestatement and proof · cited by 7,736
- Fintype.cardstatement and proof · cited by 1,386
- Fintype.card_finproof · cited by 270
- SimpleGraph.CliqueFreestatement · cited by 70
- SimpleGraph.completeGraphproof · cited by 49
- SimpleGraph.Copyproof · cited by 49
- SimpleGraph.completeMultipartiteGraphstatement and proof · cited by 11
- Fintype.exists_ne_map_eq_of_card_ltproof · cited by 7
- SimpleGraph.Embedding.map_adj_iffproof · cited by 6
- SimpleGraph.top_adjproof · cited by 5
- SimpleGraph.Copy.topEmbeddingproof · cited by 4
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