Complex sentence: The branchwidth of "G" is the minimum width of any branch-decomposition of "G"; branchwidth is closely related to tree-width and many graph optimization problems may be solved efficiently for graphs of small branchwidth.
Split into simpler sentences: The branchwidth of "G" is the minimum width of any branch-decomposition of "G". Branchwidth is closely related to tree-width and many graph optimization problems may be solved efficiently for graphs of small branchwidth.