Theorems · Definition · combinatorics
Graph.induce
{α : Type u_1} → {β : Type u_2} → Graph α β → Set α → Graph α βThe subgraph of G induced by a set X of vertices.
The edges are the edges of G with both ends in X.
(X is not required to be a subset of V(G) for this definition to work,
even though this is the standard use case)
- Defined in
- Mathlib.Combinatorics.Graph.Delete
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Set.ofPredproof · cited by 6,101
- Graphstatement and proof · cited by 242
- Graph.IsLinkproof · cited by 124
Cited by9
Results whose statement or proof uses this declaration.
- Graph.deleteVertsproof · cited by 5
- Graph.induce_lestatement and proof · cited by 2
- Graph.induce_isLinkstatement and proof · cited by 1
- Graph.induce_vertexSetstatement and proof · cited by 1
- Graph.deleteVerts_emptyproof · cited by 0
- Graph.induce_le_iffstatement and proof · cited by 0
- Graph.vertexSet_deleteVertsproof · cited by 0
- Graph.vertexSet_inducestatement and proof · cited by 0
- Graph.edgeSet_inducestatement · cited by 0