Theorems · Definition · combinatorics
SimpleGraph.ConnectedComponent.toSimpleGraph
{V : Type u} → {G : SimpleGraph V} → (C : G.ConnectedComponent) → SimpleGraph ↥CGiven a connected component C of a simple graph G, produce the induced graph on C.
The declaration connected_toSimpleGraph shows it is connected, and toSimpleGraph_hom
provides the homomorphism back to G.
- Cited by
- 14 results in Mathlib
- Foundations
- Depth 18 from the axioms · uses propext, 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.
- SimpleGraphstatement and proof · cited by 3,072
- SimpleGraph.ConnectedComponentstatement and proof · cited by 86
- SimpleGraph.induceproof · cited by 80
- SimpleGraph.ConnectedComponent.suppproof · cited by 42
Cited by16
Results whose statement or proof uses this declaration.
- SimpleGraph.ConnectedComponent.connected_toSimpleGraphstatement and proof · cited by 6
- SimpleGraph.ConnectedComponent.toSimpleGraph_homstatement · cited by 3
- SimpleGraph.homOfConnectedComponentsstatement and proof · cited by 2
- SimpleGraph.colorable_iff_forall_connectedComponentstatement and proof · cited by 2
- SimpleGraph.ConnectedComponent.adj_spanningCoe_toSimpleGraphstatement and proof · cited by 1
- SimpleGraph.ConnectedComponent.coe_toSubgraphstatement · cited by 1
- SimpleGraph.ConnectedComponent.reachable_toSimpleGraphstatement · cited by 1
- SimpleGraph.exists_isTutteViolatorproof · cited by 1
- SimpleGraph.homOfConnectedComponents_applystatement and proof · cited by 0
- SimpleGraph.colorable_iff_forall_connectedComponentsstatement · cited by 0
- SimpleGraph.ConnectedComponent.toSimpleGraph_hom_applystatement · cited by 0
- SimpleGraph.IsCycles.toSimpleGraphstatement and proof · cited by 0