Tree Decompositions

A tree decomposition is a way to break down a complex graph into simpler parts using a tree structure. Each part, called a "bag," contains some of the graph's vertices (points) and ensures that if two vertices are connected in the graph, they are also in at least one common bag. This decomposition helps solve problems in computer science, particularly in areas like network design and database theory, by allowing us to analyze and process large and complicated structures more easily and efficiently. Essentially, it organizes data for better understanding and manipulation.