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：本文研究关于固定可数图G的以下相关计算任务的复杂性：1. 输入的可数图H是否包含（导出）子图同构于G？2. 给定包含（导出）子图同构于G的可数图H，找出这样一个子图。我们的研究框架基于有效Wadge可归约性和Weihrauch可归约性。本文延续了BeMent、Hirst和Wallace在《有限复杂度理论驱动的逆向数学与Weihrauch分析》（Computability, 2021）中的工作，并解答了其中若干未解决问题。