Search for Tree Decomposition in a Spanning Subgraph with a Bounded Tree-width

The idea of ​​FPT (Fixed-Parameter Tractable), a parameterized approach to assessing the complexity of tasks and algorithms, was proposed at the end of the last century. Over the past twenty years, this idea has been developed in various fields of computer science. Among the tasks implemented using FPT-algorithms, NP-hard problems are of most interest, since theoretically these problems can be solved in polynomial time with a limited or fixed value of the parameter. One such parameter is the wood width. Wood width and wood expansions are important concepts in the development of graph algorithms. The relevance of the study of wood width and wood composition is justified by the possibility of efficient use of wood decompositions in solving NP-difficult problems (such algorithms are built in two stages - first, good wood decomposition is sought, and then the problem itself is solved on it) and using wood width as a parameter for FPT algorithms. The result of my work is a description of the algorithm for finding the spanning subgraph of a given tree width, the definition of a tree decomposition for it, a software implementation of the algorithm in Python that works exponentially with respect to the value of the tree width.