Theorems · Theorem · combinatorics
Graph.IsClosedSubgraph.adj_congr
∀ {α : Type u_1} {β : Type u_2} {x y : α} {G H : Graph α β},
x ∈ H.vertexSet → H.IsClosedSubgraph G → (H.Adj x y ↔ G.Adj x y)- Defined in
- Mathlib.Combinatorics.Graph.Subgraph
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Graphstatement and proof · cited by 242
- Graph.IsLinkproof · cited by 124
- Graph.vertexSetstatement and proof · cited by 87
- Graph.Adjstatement and proof · cited by 23
- Graph.IsClosedSubgraphstatement and proof · cited by 17
- Graph.IsInducedSubgraph.leproof · cited by 12
- Graph.IsClosedSubgraph.isInducedSubgraphproof · cited by 6
- Graph.IsLink.adjproof · cited by 5
- Graph.Adj.monoproof · cited by 4
- Graph.IsClosedSubgraph.isLink_congrproof · cited by 3
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