Theorems · Definition · combinatorics
SimpleGraph.Embedding.induce
{V : Type u_1} → {G : SimpleGraph V} → (s : Set V) → SimpleGraph.induce s G ↪g GInduced graphs embed in the original graph.
Note that if G.induce s = ⊤ (i.e., if s is a clique) then this gives the embedding of a
complete graph.
- Defined in
- Mathlib.Combinatorics.SimpleGraph.Maps
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 15 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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.Elemstatement · cited by 7,166
- SimpleGraphstatement and proof · cited by 3,072
- Function.Embedding.subtypeproof · cited by 128
- SimpleGraph.inducestatement · cited by 80
- SimpleGraph.Embeddingstatement · cited by 41
- SimpleGraph.Embedding.comapproof · cited by 2
Cited by8
Results whose statement or proof uses this declaration.
- SimpleGraph.topEmbeddingOfNotCliqueFreeproof · cited by 2
- SimpleGraph.ConnectedComponent.maximal_connected_induce_suppproof · cited by 1
- SimpleGraph.Coloring.surjOn_of_card_le_isCliqueproof · cited by 1
- SimpleGraph.Copy.induceproof · cited by 1
- SimpleGraph.ConnectedComponent.maximal_connected_induce_iffproof · cited by 0
- SimpleGraph.Walk.map_inducestatement · cited by 0
- SimpleGraph.maxDegree_induce_of_support_subsetproof · cited by 0
- SimpleGraph.isIndContained_iff_exists_iso_induceproof · cited by 0