Theorems · Theorem · combinatorics

SimpleGraph.edgeFinset_deleteIncidenceSet_eq_filter

∀ {V : Type u_1} [inst : Fintype V] [inst_1 : DecidableEq V] (G : SimpleGraph V) [inst_2 : DecidableRel G.Adj] (x : V),
  (G.deleteIncidenceSet x).edgeFinset = {x_1 ∈ G.edgeFinset | x ∉ x_1}

Deleting the incident set of the vertex x is equivalent to filtering the edges of the simple graph G that do not contain x.

Defined in

Mathlib.Combinatorics.SimpleGraph.DeleteEdges

Cited by

1 results in Mathlib

Foundations

Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FintypeDecidableEqDecidableRel