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Theorems · Theorem · combinatorics

Graph.IsClosedSubgraph.mem_iff_of_adj

∀ {α : Type u_1} {β : Type u_2} {x y : α} {G H : Graph α β},
  G.Adj x y → H.IsClosedSubgraph G → (x ∈ H.vertexSet ↔ y ∈ H.vertexSet)
Defined in
Mathlib.Combinatorics.Graph.Subgraph
Cited by
1 results in Mathlib
Foundations
Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Graph.IsInducedSubgraph.not_isClosedSubgraph_iff_exists_adj · cited by 1IsInducedSubgraph.not_isC…Set · cited by 53352SetGraph · cited by 242GraphGraph.vertexSet · cited by 87Graph.vertexSetGraph.Adj · cited by 23Graph.AdjGraph.IsClosedSubgraph · cited by 17Graph.IsClosedSubgraphGraph.IsClosedSubgraph.mem_iff_of_isLink · cited by 2IsClosedSubgraph.mem_iff_…IsClosedSubgraph.mem_iff_of_a…CITED BYCITES

Cites6

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Cited by1

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