Theorems · Theorem · combinatorics
SimpleGraph.extremalNumber_top
∀ {n : ℕ} {α : Type u_2} [inst : Fintype α] [Nontrivial α],
SimpleGraph.extremalNumber n ⊤ = (SimpleGraph.turanGraph n (Fintype.card α - 1)).edgeFinset.cardThe extremal numbers of ⊤ are equal to the number of edges in turanGraph.
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- 0 results in Mathlib
- Foundations
- Depth 92 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- FintypeNontrivial
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Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Top.topstatement and proof · cited by 9,680
- Fintypestatement and proof · cited by 7,736
- SimpleGraphstatement and proof · cited by 3,072
- Nontrivialstatement and proof · cited by 2,416
- Finset.cardstatement and proof · cited by 2,327
- Fintype.cardstatement and proof · cited by 1,386
- Sym2statement · cited by 737
- Fintype.card_finproof · cited by 270
- SimpleGraph.edgeFinsetstatement and proof · cited by 116
- SimpleGraph.extremalNumberstatement and proof · cited by 23
- SimpleGraph.turanGraphstatement and proof · cited by 14
- SimpleGraph.card_edgeFinset_of_isExtremal_freeproof · cited by 1
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