Given graph G = (V,E) I need to solve some problems that are NP-Complete on G. However it could be that G belongs to some class where these problems has polynomial solutions (here is a great resource on graph classes http://www.graphclasses.org). How can I know if G belong to some of these classes? Do I need to read and code algorithms from each paper to check it? Or there exists already an implementation for most of these algorithms?
Thanks in advance.
Edit: Maybe it is too broad my question but in some sense I want to know if someone is trying to code all these theoretic algorithms. As a reformulation of my question: Does exist some project with the goal of unify all this theoretical knowledge in practical application (real code implementation)?