Theorems · Theorem · combinatorics

SimpleGraph.degree_induce_of_support_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], G.support ⊆ s → ∀ (v : ↑s), (SimpleGraph.induce s G).degree v = G.degree ↑v

If the support of the simple graph G is a subset of the set s, then the degree of vertices in the induced subgraph of s are the same as in G.

Defined in

Mathlib.Combinatorics.SimpleGraph.Finite

Cited by

1 results in Mathlib

Foundations

Depth 63 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

DecidablePredFintypeDecidableRel