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Theorems · Theorem · combinatorics

SimpleGraph.IsTuranMaximal.isEquipartition

∀ {V : Type u_1} [inst : Fintype V] {G : SimpleGraph V} [inst_1 : DecidableRel G.Adj] {r : ℕ} (h : G.IsTuranMaximal r)
  [inst_2 : DecidableEq V], h.finpartition.IsEquipartition

The parts of a Turán-maximal graph form an equipartition.

Defined in
Mathlib.Combinatorics.SimpleGraph.Extremal.Turan
Cited by
1 results in Mathlib
Foundations
Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
FintypeDecidableRelDecidableEq
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

SimpleGraph.IsTuranMaximal.nonempty_iso_turanGraph · cited by 3IsTuranMaximal.nonempty_i…Finset · cited by 13712FinsetFintype · cited by 7736FintypeFinset.univ · cited by 3473Finset.univSimpleGraph · cited by 3072SimpleGraphFinset.card · cited by 2327Finset.cardFintype.card · cited by 1386Fintype.cardSimpleGraph.Adj · cited by 1346SimpleGraph.AdjFinpartition · cited by 199FinpartitionFinpartition.parts · cited by 184Finpartition.partsFinset.card_le_card · cited by 118Finset.card_le_cardSimpleGraph.edgeFinset · cited by 116SimpleGraph.edgeFinsetSimpleGraph.degree · cited by 112SimpleGraph.degreeSimpleGraph.CliqueFree · cited by 70SimpleGraph.CliqueFreeFinset.subset_univ · cited by 60Finset.subset_univFinpartition.IsEquipartition · cited by 45Finpartition.IsEquipartit…IsTuranMaximal.isEquipartitionCITED BYCITES

Cites26

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Cited by1

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