OAI/NumberTheory/TwoPoint/Walks/ForestRepresentation.lean
2 declarations, 0 contain sorry, 0 declared as axioms
Every finite acyclic graph has a labeled ordered-forest representation.
- theorem
OAI.TwoPointCorrelations.exists_forest_representationline 16Source 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
- lemma
OAI.TwoPointCorrelations.forest_representation_numNodesline 110