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Chordal intersection representations

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

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    Natural Language Statement

    Definition

    A chordal intersection representation is an indexed family of chordal graphs on the same vertex set whose edge intersection is the represented graph. Each factor is consequently a supergraph. Zero factors represent the complete simple graph.

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    1import Lax560391.ChordalGraphs
    2
    3/-!
    4---
    5title: Chordal intersection representations
    6type: definition
    7---
    8A chordal intersection representation is an indexed family of chordal
    9graphs on the same vertex set whose edge intersection is the represented
    10graph. Each factor is consequently a supergraph. Zero factors represent
    11the complete simple graph.
    12-/
    13
    14namespace Lax560391.ChordalIntersectionRepresentation
    15
    16structure ChordalIntersectionRepresentation {V : Type}
    17 (G : SimpleGraph V) (k : ℕ) where
    18 factors : Fin k → SimpleGraph V
    19 chordal : ∀ i, Lax560391.ChordalGraphs.IsChordal (factors i)
    20 represents : ∀ u v, u ≠ v → (G.Adj u v ↔ ∀ i, (factors i).Adj u v)
    21
    22end Lax560391.ChordalIntersectionRepresentation
    23
    Builds on
    Used by
    From Mathlib

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