Theorems · Theorem · combinatorics
Graph.IsSubgraph.not_isInducedSubgraph_iff
∀ {α : Type u_1} {β : Type u_2} {G H : Graph α β},
H ≤ G → (¬H.IsInducedSubgraph G ↔ ∃ e x y, G.IsLink e x y ∧ x ∈ H.vertexSet ∧ y ∈ H.vertexSet ∧ e ∉ H.edgeSet)- Defined in
- Mathlib.Combinatorics.Graph.Subgraph
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 61 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites8
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.IsLinkstatement and proof · cited by 124
- Graph.vertexSetstatement and proof · cited by 87
- Graph.edgeSetstatement and proof · cited by 79
- Graph.IsInducedSubgraphstatement and proof · cited by 16
- Graph.IsLink.edge_memproof · cited by 14
- Graph.IsInducedSubgraph.isLink_of_mem_memproof · cited by 8
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