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Characterizations Of Some Classes Of Graphs That Are Nearly Series-Parallel, Victoria Fontaine

LSU Doctoral Dissertations

A series-parallel graph can be built from a single-edge graph by a sequence of series and parallel extensions. The class of such graphs coincides with the class of graphs that do not have the complete graph K₄ as a minor. This dissertation considers a class M₁ of graphs that are close to being series-parallel. In particular, every member of the class has the property that one can obtain a series-parallel graph by adding a new edge and contracting it out, or by splitting a vertex into two vertices whose neighbor sets partition the neighbor set of the original …