High Quality Content by WIKIPEDIA articles! In graph theory, series-parallel graphs are graphs with two distinguished vertices called terminals, formed recursively by two simple composition operations. They can be used to model series and parallel electric circuits. Every series-parallel graph has treewidth at most 2. Indeed, a graph has treewidth at most 2 if and only if every biconnected component is a series-parallel graph.[3] Graphs of treewidth at most 2 have an explicit forbidden minor characterization, implying that a graph is series-parallel if and only if its biconnected components are linked in a path and it excludes the complete graph K4 as a minor.

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