Theorems · Theorem · combinatorics
Graph.IsInducedSubgraph.not_isClosedSubgraph_iff_exists_adj
∀ {α : Type u_1} {β : Type u_2} {G H : Graph α β},
H.IsInducedSubgraph G → (¬H.IsClosedSubgraph G ↔ ∃ x y, G.Adj x y ∧ x ∈ H.vertexSet ∧ y ∉ H.vertexSet)- Defined in
- Mathlib.Combinatorics.Graph.Subgraph
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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.edgeSetproof · cited by 79
- Graph.Incproof · cited by 42
- Graph.Adjstatement and proof · cited by 23
- Graph.IsClosedSubgraphstatement and proof · cited by 17
- Graph.IsInducedSubgraphstatement and proof · cited by 16
- Graph.IsLink.edge_memproof · cited by 14
- Graph.IsInducedSubgraph.isLink_of_mem_memproof · cited by 8
- Graph.IsClosedSubgraph.mem_iff_of_adjproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Graph.IsInducedSubgraph.not_isClosedSubgraph_iff_exists_isLinkproof · cited by 0