Mathlib Map

Theorems · Definition · combinatorics

SimpleGraph.extremalNumber

ℕ → {W : Type u_1} → SimpleGraph W → ℕ

The extremal number of a natural number n and a simple graph H is the maximum number of edges in a H-free simple graph on n vertices. If H is contained in all simple graphs on n vertices, then this is 0.

Defined in
Mathlib.Combinatorics.SimpleGraph.Extremal.Basic
Cited by
23 results in Mathlib
Foundations
Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound

Around this declaration

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

SimpleGraph.card_edgeFinset_le_extremalNumber · cited by 6SimpleGraph.card_edgeFins…SimpleGraph.turanDensity · cited by 6SimpleGraph.turanDensitySimpleGraph.extremalNumber_le_iff · cited by 4SimpleGraph.extremalNumbe…SimpleGraph.extremalNumber_of_fintypeCard_eq · cited by 3SimpleGraph.extremalNumbe…SimpleGraph.antitoneOn_extremalNumber_div_choose_two · cited by 3SimpleGraph.antitoneOn_ex…SimpleGraph.extremalNumber_le_iff_of_nonneg · cited by 2SimpleGraph.extremalNumbe…SimpleGraph.isExtremal_free_iff · cited by 2SimpleGraph.isExtremal_fr…SimpleGraph.isGLB_turanDensity · cited by 2SimpleGraph.isGLB_turanDe…SimpleGraph.IsContained.of_extremalNumber_lt_card_edgeFinset · cited by 1IsContained.of_extremalNu…SimpleGraph.eventually_isContained_of_card_edgeFinset · cited by 1SimpleGraph.eventually_is…SimpleGraph.card_edgeFinset_deleteIncidenceSet_le_extremalNumber · cited by 1SimpleGraph.card_edgeFins…SimpleGraph.card_edgeFinset_of_isExtremal_free · cited by 1SimpleGraph.card_edgeFins…SimpleGraph.extremalNumber_congr · cited by 1SimpleGraph.extremalNumbe…SimpleGraph.tendsto_turanDensity · cited by 1SimpleGraph.tendsto_turan…SimpleGraph.lt_extremalNumber_iff · cited by 1SimpleGraph.lt_extremalNu…Finset.univ · cited by 3473Finset.univSimpleGraph · cited by 3072SimpleGraphFinset.card · cited by 2327Finset.cardFinset.filter · cited by 949Finset.filterFinset.sup · cited by 530Finset.supSimpleGraph.edgeFinset · cited by 116SimpleGraph.edgeFinsetSimpleGraph.Free · cited by 39SimpleGraph.FreeSimpleGraph.extremalNumberCITED BYCITES

Cites7

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by24

Results whose statement or proof uses this declaration.