Theorems · Theorem · combinatorics
SimpleGraph.degree_eq_one_iff_existsUnique_adj
∀ {V : Type u_1} {G : SimpleGraph V} {v : V} [inst : Fintype ↑(G.neighborSet v)], G.degree v = 1 ↔ ∃! w, G.Adj v w- Defined in
- Mathlib.Combinatorics.SimpleGraph.Finite
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 60 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Fintype
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Fintypestatement and proof · cited by 7,736
- Set.Elemstatement and proof · cited by 7,166
- SimpleGraphstatement and proof · cited by 3,072
- SimpleGraph.Adjstatement and proof · cited by 1,346
- ExistsUniquestatement and proof · cited by 268
- SimpleGraph.neighborSetstatement and proof · cited by 257
- SimpleGraph.degreestatement · cited by 112
- SimpleGraph.neighborFinsetproof · cited by 72
- Finset.card_eq_oneproof · cited by 16
- Finset.singleton_iff_unique_memproof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- SimpleGraph.Connected.induce_compl_singleton_of_degree_eq_oneproof · cited by 1
- SimpleGraph.degree_starGraph_of_ne_centerproof · cited by 0
- SimpleGraph.IsTree.exists_ne_and_degree_eq_oneproof · cited by 0