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Cochromatic partitions

Lax560391.CochromaticPartition · concepts/Lax560391/CochromaticPartition.lean · lax-560391

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    Natural Language Statement

    Definition

    A cochromatic partition assigns each vertex a part, each part inducing either a clique or an independent set. Empty labels are allowed. Parts need not be modules.

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    1import Mathlib.Combinatorics.SimpleGraph.Basic
    2
    3/-!
    4---
    5title: Cochromatic partitions
    6type: definition
    7---
    8A cochromatic partition assigns each vertex a part, each part inducing
    9either a clique or an independent set. Empty labels are allowed. Parts need
    10not be modules.
    11-/
    12
    13namespace Lax560391.CochromaticPartition
    14
    15structure CochromaticPartition {V : Type} (G : SimpleGraph V) (k : ℕ) where
    16 part : V → Fin k
    17 homogeneous : ∀ i,
    18 (∀ u v, u ≠ v → part u = i → part v = i → G.Adj u v) ∨
    19 (∀ u v, part u = i → part v = i → ¬ G.Adj u v)
    20
    21end Lax560391.CochromaticPartition
    22
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