Mathlib Map

Theorems · Definition · combinatorics

SimpleGraph.IsTuranMaximal

{V : Type u_1} → [Fintype V] → (G : SimpleGraph V) → [DecidableRel G.Adj] → ℕ → Prop

An r + 1-cliquefree graph is r-Turán-maximal if any other r + 1-cliquefree graph on the same vertex set has the same or fewer number of edges.

Defined in
Mathlib.Combinatorics.SimpleGraph.Extremal.Turan
Cited by
19 results in Mathlib
Foundations
Depth 66 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.

SimpleGraph.IsTuranMaximal.finpartition · cited by 7IsTuranMaximal.finpartiti…SimpleGraph.IsTuranMaximal.not_adj_iff_part_eq · cited by 4IsTuranMaximal.not_adj_if…SimpleGraph.isTuranMaximal_of_iso · cited by 3SimpleGraph.isTuranMaxima…SimpleGraph.IsTuranMaximal.nonempty_iso_turanGraph · cited by 3IsTuranMaximal.nonempty_i…SimpleGraph.isTuranMaximal_iff_nonempty_iso_turanGraph · cited by 2SimpleGraph.isTuranMaxima…SimpleGraph.exists_isTuranMaximal · cited by 2SimpleGraph.exists_isTura…SimpleGraph.isExtremal_top_free_iff_isTuranMaximal · cited by 2SimpleGraph.isExtremal_to…SimpleGraph.isTuranMaximal_turanGraph · cited by 1SimpleGraph.isTuranMaxima…SimpleGraph.IsTuranMaximal.card_parts · cited by 1IsTuranMaximal.card_partsSimpleGraph.IsTuranMaximal.card_parts_le · cited by 1IsTuranMaximal.card_parts…SimpleGraph.IsTuranMaximal.degree_eq_card_sub_part_card · cited by 1IsTuranMaximal.degree_eq_…SimpleGraph.IsTuranMaximal.degree_eq_of_not_adj · cited by 1IsTuranMaximal.degree_eq_…SimpleGraph.IsTuranMaximal.isEquipartition · cited by 1IsTuranMaximal.isEquipart…SimpleGraph.IsTuranMaximal.not_adj_trans · cited by 1IsTuranMaximal.not_adj_tr…SimpleGraph.IsTuranMaximal.setoid · cited by 1IsTuranMaximal.setoidFintype · cited by 7736FintypeSimpleGraph · cited by 3072SimpleGraphSimpleGraph.Adj · cited by 1346SimpleGraph.AdjSimpleGraph.CliqueFree · cited by 70SimpleGraph.CliqueFreeSimpleGraph.IsExtremal · cited by 9SimpleGraph.IsExtremalSimpleGraph.IsTuranMaximalCITED BYCITES

Cites5

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Cited by21

Results whose statement or proof uses this declaration.