Theorems · Theorem · combinatorics

SimpleGraph.degree_induce_of_neighborSet_subset

∀ {V : Type u_1} {s : Set V} [inst : DecidablePred fun x => x ∈ s] [inst_1 : Fintype V] {G : SimpleGraph V}
  [inst_2 : DecidableRel G.Adj] {v : ↑s}, G.neighborSet ↑v ⊆ s → (SimpleGraph.induce s G).degree v = G.degree ↑v

If the neighbor set of a vertex v is a subset of s, then the degree of the vertex in the induced subgraph of s is the same as in G.

Defined in

Mathlib.Combinatorics.SimpleGraph.Finite

Cited by

3 results in Mathlib

Foundations

Depth 62 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

DecidablePredFintypeDecidableRel