Theorems · Definition · combinatorics
SimpleGraph.neighborFinset
{V : Type u_1} → (G : SimpleGraph V) → (v : V) → [Fintype ↑(G.neighborSet v)] → Finset VG.neighborFinset v is the Finset version of G.neighborSet v in case G is
locally finite at v.
- Defined in
- Mathlib.Combinatorics.SimpleGraph.Finite
- Cited by
- 72 results in Mathlib
- Foundations
- Depth 28 from the axioms · uses propext, Quot.sound
- Assumes
- Fintype
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement · 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
- SimpleGraph.neighborSetstatement and proof · cited by 257
- Set.toFinsetproof · cited by 217
Cited by73
Results whose statement or proof uses this declaration.
- SimpleGraph.degreeproof · cited by 112
- SimpleGraph.coe_neighborFinsetstatement · cited by 9
- SimpleGraph.mem_neighborFinsetstatement · cited by 6
- SimpleGraph.neighborFinset_eq_filterstatement · cited by 6
- SimpleGraph.card_neighborFinset_eq_degreestatement · cited by 5
- SimpleGraph.notMem_neighborFinset_selfstatement · cited by 4
- SimpleGraph.adjMatrix_mulVec_applystatement and proof · cited by 4
- SimpleGraph.degree_eq_one_iff_existsUnique_adjproof · cited by 3
- SimpleGraph.degree_induce_of_neighborSet_subsetproof · cited by 3
- SimpleGraph.neighborFinset_defstatement · cited by 3
- SimpleGraph.IsSRGWith.card_neighborFinset_union_eqstatement and proof · cited by 2
- SimpleGraph.compl_neighborFinset_sdiff_inter_eqstatement · cited by 2