  We study the complexity of the following related computational tasks
concerning a fixed countable graph G: 1. Does a countable graph H provided as
input have a(n induced) subgraph isomorphic to G? 2. Given a countable graph H
that has a(n induced) subgraph isomorphic to G, find such a subgraph. The
framework for our investigations is given by effective Wadge reducibility and
by Weihrauch reducibility. Our work follows on "Reverse mathematics and
Weihrauch analysis motivated by finite complexity theory" (Computability, 2021)
by BeMent, Hirst and Wallace, and we answer several of their open questions.
