Theorems · Theorem · combinatorics

SimpleGraph.zarankiewicz_le_extremalNumber

∀ {m n s t : ℕ} {α : Type u_3} {β : Type u_4} [inst : Fintype α] [inst_1 : Fintype β],
  Fintype.card α = s →
    Fintype.card β = t →
      SimpleGraph.zarankiewicz m n s t ≤ SimpleGraph.extremalNumber (m + n) (completeBipartiteGraph α β)

The Zarankiewicz function is at most the corresponding extremal number.

Defined in

Mathlib.Combinatorics.SimpleGraph.Extremal.Zarankiewicz

Cited by

0 results in Mathlib

Foundations

Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FintypeFintype