FormalConjecturesForMathlib.Combinatorics.SimpleGraph.Prod

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module

public import Mathlib.Combinatorics.SimpleGraph.Prod

@[expose] public section

Decidable adjacency in box products

Adjacency in G □ H is decidable when adjacency in G and H is and the vertex types have decidable equality. This lets decide handle finite questions about box products.

namespace SimpleGraphvariable {α β : Type*} [DecidableEq α] [DecidableEq β] (G : SimpleGraph α) (H : SimpleGraph β)

Adjacency in a box product of graphs with decidable adjacency is decidable.

instance boxProd.decidableRel [DecidableRel G.Adj] [DecidableRel H.Adj] :
    DecidableRel (G □ H).Adj :=
  fun _ _ => decidable_of_iff _ boxProd_adj.symm

end SimpleGraph