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Theorems · Theorem · combinatorics

SimpleGraph.IsAcyclic.subgraph

∀ {V : Type u_1} {G : SimpleGraph V}, G.IsAcyclic → ∀ (H : G.Subgraph), H.coe.IsAcyclic

A subgraph of an acyclic graph is acyclic.

Defined in
Mathlib.Combinatorics.SimpleGraph.Acyclic
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Foundations
Depth 27 from the axioms · uses propext, Quot.sound
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Set.Elem · cited by 7166Set.ElemSimpleGraph · cited by 3072SimpleGraphSimpleGraph.Subgraph · cited by 326SimpleGraph.SubgraphSimpleGraph.Subgraph.verts · cited by 210Subgraph.vertsSimpleGraph.Subgraph.coe · cited by 89Subgraph.coeSimpleGraph.IsAcyclic · cited by 67SimpleGraph.IsAcyclicSimpleGraph.Subgraph.hom · cited by 18Subgraph.homSimpleGraph.IsAcyclic.comap · cited by 4IsAcyclic.comapSimpleGraph.Subgraph.hom_injective · cited by 2Subgraph.hom_injectiveIsAcyclic.subgraphCITED BYCITES

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