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f0f05de | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 | import Mathlib.Combinatorics.Hypergraph.Basic
import Mathlib.Data.Finset.Card
import Mathlib.Data.Finset.Pi
import Mathlib.Data.Nat.Prime.Defs
import OAI.Combinatorics.BalancedRyser.Model
namespace OAI
namespace Balanced
open scoped _root_.Balanced
namespace PartiteHypergraph
variable {r n : ℕ}
def part (i : Fin r) : Finset (Vertex r n) :=
Finset.univ.image (fun v : Fin n => (i, v))
def edgeVertices (e : Fin r → Fin n) : Finset (Vertex r n) :=
Finset.univ.image (fun i : Fin r => (i, e i))
def toHypergraph (H : PartiteHypergraph r n) : Hypergraph (Vertex r n) where
vertexSet := Set.univ
edgeSet := {E | ∃ e ∈ H.edges, E = ↑(edgeVertices e)}
subset_vertexSet_of_mem_edgeSet' := fun _ _ => Set.subset_univ _
def IsMatching (H : PartiteHypergraph r n) (M : Finset (Fin r → Fin n)) : Prop :=
M ⊆ H.edges ∧
∀ e ∈ M, ∀ f ∈ M, e ≠ f → Disjoint (edgeVertices e) (edgeVertices f)
end PartiteHypergraph
end Balanced
end OAI
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