Theorems · Theorem · combinatorics
SimpleGraph.Subgraph.degree_eq_one_iff_existsUnique_adj
∀ {V : Type u} {G : SimpleGraph V} {G' : G.Subgraph} {v : V} [inst : Fintype ↑(G'.neighborSet v)],
G'.degree v = 1 ↔ ∃! w, G'.Adj v w- Cited by
- 0 results in Mathlib
- Foundations
- Depth 59 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Fintype
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Cites12
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.Subgraphstatement and proof · cited by 326
- ExistsUniquestatement and proof · cited by 268
- Set.toFinsetproof · cited by 217
- SimpleGraph.Subgraph.Adjstatement and proof · cited by 147
- SimpleGraph.Subgraph.neighborSetstatement and proof · cited by 46
- Finset.card_eq_oneproof · cited by 16
- SimpleGraph.Subgraph.degreestatement · cited by 14
- Finset.singleton_iff_unique_memproof · cited by 2
- SimpleGraph.Subgraph.finset_card_neighborSet_eq_degreeproof · cited by 1
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