Theorems · Theorem · combinatorics
SimpleGraph.degree_compl
∀ {V : Type u_1} (G : SimpleGraph V) (v : V) [inst : Fintype ↑(G.neighborSet v)] [inst_1 : Fintype ↑(Gᶜ.neighborSet v)]
[inst_2 : Fintype V], Gᶜ.degree v = Fintype.card V - 1 - G.degree v- Defined in
- Mathlib.Combinatorics.SimpleGraph.Finite
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetproof · cited by 13,712
- Fintypestatement and proof · cited by 7,736
- Set.Elemstatement and proof · cited by 7,166
- SimpleGraphstatement and proof · cited by 3,072
- Compl.complstatement and proof · cited by 2,925
- Finset.cardproof · cited by 2,327
- Fintype.cardstatement · cited by 1,386
- SimpleGraph.neighborSetstatement and proof · cited by 257
- SimpleGraph.degreestatement and proof · cited by 112
- Set.toFinset_cardproof · cited by 63
- Finset.card_union_of_disjointproof · cited by 37
- SimpleGraph.card_neighborSet_eq_degreeproof · cited by 9
Cited by1
Results whose statement or proof uses this declaration.
- SimpleGraph.IsRegularOfDegree.complproof · cited by 1