Branch decomposition is a concept in graph theory that provides a way to represent a graph in a hierarchical structure, which is particularly useful for various applications, including optimization problems and parameterized complexity. ### Key Concepts of Branch-Decomposition: 1. **Definitions**: - A branch-decomposition of a graph \( G \) is a tree-like structure (called a branch tree) where each node is associated with subsets of vertices of \( G \).
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