IsUniform — Mathlib

English

If two partitions P and P' are equivalent and the graphs G,G' are equivalent, then IsUniform is preserved under ε-parameter changes.

Русский

Если разбиения P и P' эквивалентны, а графы G и G' эквивалентны, то IsUniform сохраняется при изменении параметра ε.

LaTeX

$$P.IsUniform G ε ⇔ P'.IsUniform G' ε' (при эквивалентности) $$

Lean4

/-- A finpartition of a graph's vertex set is `ε`-uniform (aka `ε`-regular) iff the proportion of
its pairs of parts that are not `ε`-uniform is at most `ε`. -/
def IsUniform (ε : 𝕜) : Prop :=
  (#(P.nonUniforms G ε) : 𝕜) ≤ (#P.parts * (#P.parts - 1) : ℕ) * ε

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