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doc(combinatorics/simple_graph/basic): mention half-edge synonym for …
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…darts (#13312)
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kmill committed Apr 11, 2022
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6 changes: 4 additions & 2 deletions src/combinatorics/simple_graph/basic.lean
Expand Up @@ -33,7 +33,7 @@ finitely many vertices.
if `incidence_set` is finite
* `simple_graph.dart` is an ordered pair of adjacent vertices, thought of as being an
orientated edge.
orientated edge. These are also known as "half-edges" or "bonds."
* `simple_graph.hom`, `simple_graph.embedding`, and `simple_graph.iso` for graph
homomorphisms, graph embeddings, and
Expand Down Expand Up @@ -321,7 +321,9 @@ instance edges_fintype [decidable_eq V] [fintype V] [decidable_rel G.adj] :

/-! ## Darts -/

/-- A `dart` is an oriented edge, implemented as an ordered pair of adjacent vertices. -/
/-- A `dart` is an oriented edge, implemented as an ordered pair of adjacent vertices.
This terminology comes from combinatorial maps, and they are also known as "half-edges"
or "bonds." -/
@[ext, derive decidable_eq]
structure dart extends V × V :=
(is_adj : G.adj fst snd)
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