Theorems · Theorem · combinatorics
SimpleGraph.IsTuranMaximal.nonempty_iso_turanGraph
∀ {V : Type u_1} [inst : Fintype V] {G : SimpleGraph V} [inst_1 : DecidableRel G.Adj] {r : ℕ},
G.IsTuranMaximal r → Nonempty (G ≃g SimpleGraph.turanGraph (Fintype.card V) r)Turán's theorem, forward direction.
Any r + 1-cliquefree Turán-maximal graph on n vertices is isomorphic to turanGraph n r.
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 88 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- FintypeDecidableRel
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites30
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Equivproof · cited by 8,337
- Fintypestatement and proof · cited by 7,736
- Equiv.symmproof · cited by 3,681
- Finset.univproof · cited by 3,473
- SimpleGraphstatement and proof · cited by 3,072
- Finset.cardproof · cited by 2,327
- LT.lt.leproof · cited by 2,189
- Fintype.cardstatement and proof · cited by 1,386
- SimpleGraph.Adjstatement and proof · cited by 1,346
- LT.lt.transproof · cited by 370
- Finset.mem_univproof · cited by 361
Cited by3
Results whose statement or proof uses this declaration.
- SimpleGraph.isTuranMaximal_of_isoproof · cited by 3
- SimpleGraph.isTuranMaximal_iff_nonempty_iso_turanGraphproof · cited by 2
- SimpleGraph.IsTuranMaximal.isoproof · cited by 0