Theorems · Theorem · combinatorics
SimpleGraph.insert_neighborFinset_eq_univ
∀ {V : Type u_1} (G : SimpleGraph V) [inst : Fintype V] [inst_1 : DecidableEq V] [inst_2 : DecidableRel G.Adj] (v : V),
insert v (G.neighborFinset v) = Finset.univ ↔ G.IsUniversal v- Defined in
- Mathlib.Combinatorics.SimpleGraph.Finite
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 60 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Finsetstatement · cited by 13,712
- Fintypestatement and proof · cited by 7,736
- Finset.univstatement and proof · cited by 3,473
- SimpleGraphstatement and proof · cited by 3,072
- SimpleGraph.Adjstatement and proof · cited by 1,346
- SimpleGraph.neighborSetstatement · cited by 257
- SimpleGraph.neighborFinsetstatement · cited by 72
- SimpleGraph.IsUniversalstatement · cited by 21
Cited by1
Results whose statement or proof uses this declaration.
- SimpleGraph.degree_eq_card_sub_oneproof · cited by 0