Theorems · Definition · combinatorics
SimpleGraph.incidenceFinset
{V : Type u_1} → (G : SimpleGraph V) → (v : V) → [Fintype ↑(G.neighborSet v)] → [DecidableEq V] → Finset (Sym2 V)This is the Finset version of incidenceSet.
- Defined in
- Mathlib.Combinatorics.SimpleGraph.Finite
- Cited by
- 15 results in Mathlib
- Foundations
- Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- FintypeDecidableEq
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- Sym2statement · cited by 737
- SimpleGraph.neighborSetstatement and proof · cited by 257
- Set.toFinsetproof · cited by 217
- SimpleGraph.incidenceSetproof · cited by 46
Cited by15
Results whose statement or proof uses this declaration.
- SimpleGraph.coe_incidenceFinsetstatement · cited by 4
- SimpleGraph.card_incidenceFinset_eq_degreestatement and proof · cited by 4
- SimpleGraph.incidenceFinset_subsetstatement · cited by 2
- SimpleGraph.edgeFinset_deleteIncidenceSet_eq_sdiffstatement and proof · cited by 2
- SimpleGraph.disjoint_sdiff_neighborFinset_imagestatement and proof · cited by 2
- SimpleGraph.card_edgeFinset_replaceVertex_of_not_adjproof · cited by 2
- SimpleGraph.Walk.IsEulerian.even_degree_iffproof · cited by 1
- SimpleGraph.mem_incidenceFinsetstatement · cited by 1
- SimpleGraph.incidenceFinset_eq_filterstatement · cited by 1
- SimpleGraph.edgeFinset_deleteIncidenceSet_eq_filterproof · cited by 1
- SimpleGraph.edgeFinset_replaceVertex_of_adjstatement and proof · cited by 1
- SimpleGraph.edgeFinset_replaceVertex_of_not_adjstatement and proof · cited by 1