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Interval representations

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

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    Natural Language Statement

    Definition

    An interval representation assigns a nonempty closed real interval to each vertex, with adjacency exactly when two distinct vertices have intersecting intervals. Point intervals and repeated intervals are allowed.

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    1import Mathlib.Combinatorics.SimpleGraph.Basic
    2import Mathlib.Data.Real.Basic
    3
    4/-!
    5---
    6title: Interval representations
    7type: definition
    8---
    9An interval representation assigns a nonempty closed real interval to each
    10vertex, with adjacency exactly when two distinct vertices have intersecting
    11intervals. Point intervals and repeated intervals are allowed.
    12-/
    13
    14namespace Lax560391.IntervalRepresentation
    15
    16structure IntervalRepresentation {V : Type} (G : SimpleGraph V) where
    17 lo : V → ℝ
    18 hi : V → ℝ
    19 nonempty : ∀ v, lo v ≤ hi v
    20 represents : ∀ u v, u ≠ v →
    21 (G.Adj u v ↔ lo u ≤ hi v ∧ lo v ≤ hi u)
    22
    23end Lax560391.IntervalRepresentation
    24
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    From Mathlib

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