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Lax68.Stars

Stars

concepts/Lax68/Stars.lean · lax-68

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    Definition

    A star has a centre adjacent to every other vertex and has no edges between two non-central vertices.

    Lean source view on GitHub

    1import Mathlib.Combinatorics.SimpleGraph.UniversalVerts
    2
    3/-!
    4---
    5title: Stars
    6type: definition
    7---
    8A star has a centre adjacent to every other vertex and has no edges between
    9two non-central vertices.
    10-/
    11
    12set_option autoImplicit false
    13
    14namespace Lax68.Stars
    15
    16def HasStarShape {V : Type*} (G : SimpleGraph V) : Prop :=
    17 ∃ centre : V,
    18 centre ∈ G.universalVerts ∧
    19 ∀ ⦃u v⦄, G.Adj u v → u = centre ∨ v = centre
    20
    21def IsStar {V : Type*} (G : SimpleGraph V) : Prop :=
    22 HasStarShape G
    23
    24end Lax68.Stars
    25

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    From Mathlib

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