[Merged by Bors] - feat: definition and properties of the Turán graph#9645
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Parcly-Taxel wants to merge 18 commits intomasterfrom
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[Merged by Bors] - feat: definition and properties of the Turán graph#9645Parcly-Taxel wants to merge 18 commits intomasterfrom
Parcly-Taxel wants to merge 18 commits intomasterfrom
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Parcly-Taxel
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Mar 20, 2024
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| convert Nat.lt.base _ | ||
| convert G.card_edgeFinset_sup_edge na ne |
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Is there a nicer way to do these steps? rw [G.card_edgeFinset_sup_edge na ne, Nat.lt.base] doesn't work because the inner instances corresponding to the Sup don't match.
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I fixed it (by generalising the fintype assumptions appearing on the LHS of earlier lemmas) and then found a golf which made the fix redundant. Here's the fixed ungolfed version for your instruction:
theorem not_cliqueFree_of_isTuranMaximal (hn : r ≤ Fintype.card V) (hG : IsTuranMaximal G r) :
¬G.CliqueFree r := by
by_contra cf
obtain ⟨K, _, rfl⟩ := exists_smaller_set (univ : Finset V) r hn
have := (G.isNClique_iff).not.mp (cf K)
simp_rw [and_true, IsClique, Set.Pairwise, not_forall] at this
obtain ⟨a, _, b, _, ne, na⟩ := this
refine not_not_intro hG ?_
simp_rw [IsTuranMaximal, hG.1, true_and]; push_neg
use G ⊔ edge a b, inferInstance, cf.sup_edge a b
rw [card_edgeFinset_sup_edge]
exacts [lt_add_one _, na, ne]
YaelDillies
reviewed
Mar 21, 2024
Co-authored-by: Yaël Dillies <yael.dillies@gmail.com>
YaelDillies
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Mar 22, 2024
Co-authored-by: Yaël Dillies <yael.dillies@gmail.com>
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Thanks! maintainer merge |
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🚀 Pull request has been placed on the maintainer queue by YaelDillies. |
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The first part of the main file in #9317. Co-authored-by: Yaël Dillies <yael.dillies@gmail.com>
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The first part of the main file in #9317. Co-authored-by: Yaël Dillies <yael.dillies@gmail.com>
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Pull request successfully merged into master. Build succeeded: |
utensil
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The first part of the main file in #9317. Co-authored-by: Yaël Dillies <yael.dillies@gmail.com>
xgenereux
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The first part of the main file in #9317. Co-authored-by: Yaël Dillies <yael.dillies@gmail.com>
atarnoam
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The first part of the main file in #9317. Co-authored-by: Yaël Dillies <yael.dillies@gmail.com>
uniwuni
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The first part of the main file in #9317. Co-authored-by: Yaël Dillies <yael.dillies@gmail.com>
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The first part of the main file in #9317. Co-authored-by: Yaël Dillies <yael.dillies@gmail.com>
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The first part of the main file in #9317.