Theorems · Theorem · combinatorics
Graph.exists_eq_bouquet
∀ {α : Type u_1} {β : Type u_2} {G : Graph α β},
G.vertexSet.Nonempty → G.vertexSet.Subsingleton → ∃ x F, G = Graph.bouquet x FEvery graph on just one vertex is a bouquet on that vertex.
- Defined in
- Mathlib.Combinatorics.Graph.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 24 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Set.Nonemptystatement and proof · cited by 2,627
- Set.Subsingletonstatement and proof · cited by 276
- Graphstatement and proof · cited by 242
- Graph.vertexSetstatement and proof · cited by 87
- Graph.edgeSetproof · cited by 79
- Set.Nonempty.someproof · cited by 53
- Set.Nonempty.some_memproof · cited by 42
- Graph.bouquetstatement · cited by 11
- Graph.eq_bouquet_of_subsingletonproof · cited by 2
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