Theorems · Definition · combinatorics
SimpleGraph.Embedding
{V : Type u_1} → {W : Type u_2} → SimpleGraph V → SimpleGraph W → Type (max u_1 u_2)A graph embedding is an embedding f such that for vertices v w : V,
G'.Adj (f v) (f w) ↔ G.Adj v w. Its image is an induced subgraph of G'.
The notation G ↪g G' represents the type of graph embeddings.
- Defined in
- Mathlib.Combinatorics.SimpleGraph.Maps
- Cited by
- 41 results in Mathlib
- Foundations
- Depth 2 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
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.Adjproof · cited by 1,346
- RelEmbeddingproof · cited by 281
Cited by73
Results whose statement or proof uses this declaration.
- SimpleGraph.IsIndContainedproof · cited by 22
- SimpleGraph.Embedding.toHomstatement and proof · cited by 17
- SimpleGraph.Embedding.compstatement and proof · cited by 10
- SimpleGraph.Embedding.completeGraphstatement · cited by 9
- SimpleGraph.Iso.toEmbeddingstatement · cited by 9
- SimpleGraph.Embedding.toCopystatement and proof · cited by 7
- SimpleGraph.Embedding.inducestatement · cited by 6
- SimpleGraph.Embedding.map_adj_iffstatement and proof · cited by 6
- SimpleGraph.induceHomOfLEstatement · cited by 5
- SimpleGraph.Embedding.sumstatement and proof · cited by 5
- SimpleGraph.completeMultipartiteGraph.topEmbeddingstatement · cited by 4
- SimpleGraph.Copy.topEmbeddingstatement · cited by 4