Theorems · Theorem · combinatorics
SimpleGraph.card_edgeFinset_induce_compl_singleton
∀ {V : Type u_1} [inst : Fintype V] [inst_1 : DecidableEq V] (G : SimpleGraph V) [inst_2 : DecidableRel G.Adj] (x : V),
(SimpleGraph.induce {x}ᶜ G).edgeFinset.card = (G.deleteIncidenceSet x).edgeFinset.cardDeleting the incidence set of the vertex x retains the same number of edges as in the induced
subgraph of the vertices {x}ᶜ.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites27
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Setstatement and proof · cited by 53,352
- 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.cardstatement · cited by 2,327
- Fintype.cardproof · cited by 1,386
- SimpleGraph.Adjstatement and proof · cited by 1,346
- Function.Embeddingstatement · cited by 988
- Sym2statement · cited by 737
- Set.subset_univproof · cited by 228
Cited by1
Results whose statement or proof uses this declaration.
- SimpleGraph.card_edgeFinset_deleteIncidenceSet_le_extremalNumberproof · cited by 1