induce — Mathlib

English

Inducing a graph to a subset s of vertices yields the restricted graph on s.

Русский

Воздействие графа на подмножество вершин s даёт граф, ограниченный на s.

LaTeX

$$$ \\operatorname{induce}(s,G) = G \\!\\restriction_{s} \\, = \\, G\\,\\mathrm{comap}(\\mathrm{Embedding.subtype}_s) $$$

Lean4

/-- Restrict a graph to the vertices in the set `s`, deleting all edges incident to vertices
outside the set. This is a wrapper around `SimpleGraph.comap`. -/
abbrev induce (s : Set V) (G : SimpleGraph V) : SimpleGraph s :=
  G.comap (Function.Embedding.subtype _)

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