OAI/NumberTheory/TwoPoint/Walks/ForestRepresentation.lean

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2 declarations, 0 contain sorry, 0 declared as axioms

Every finite acyclic graph has a labeled ordered-forest representation.

  1. theorem OAI.TwoPointCorrelations.exists_forest_representation line 16

    Source documentation

    The labels are a permutation of the vertices and adjacency is exactly parent/child incidence in the ordered forest.

    theorem exists_forest_representation {V : Type u} [Fintype V]
        (G : SimpleGraph V) (hG : G.IsAcyclic) :
        ∃ t : BinaryTree V, (forestNodes t).Nodup ∧ (∀ v, v ∈ forestNodes t) ∧
          ∀ a b, forestAdjacent t a b ↔ G.Adj a b := by
    …

    Mentions: OAI.TwoPointCorrelations.forestNodes, OAI.TwoPointCorrelations.forestAdjacent

  2. lemma OAI.TwoPointCorrelations.forest_representation_numNodes line 110