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.

翻译：我们研究以下与固定可数图G相关的计算任务的复杂性：1. 给定作为输入的可数图H，它是否包含一个（导出）子图同构于G？2. 给定一个含有（导出）子图同构于G的可数图H，找出这样一个子图。我们的研究框架由有效Wadge可归约性和Weihrauch可归约性提供。本研究延续了BeMent、Hirst和Wallace在《反向数学与受有限复杂性理论启发的Weihrauch分析》（Computability, 2021）中的工作，并回答了他们的若干开放问题。