On the Vertex Separation of Cactus Graphs

This paper is part of a work in progress whose goal is to construct a fast, practical algorithm for the vertex separation (VS) of cactus graphs. We prove a \main theorem for cacti", a necessary and sufficient condition for the VS of a cactus graph being k. Further, we investigate the ensuing ramifications that prevent the construction of an algorithm based on that theorem only.

On the Vertex Separation of Maximal Outerplanar Graphs

We investigate the NP-complete problem Vertex Separation (VS) on Maximal Outerplanar Graphs (mops). We formulate and prove a “main theorem for mops”, a necessary and sufficient condition for the vertex separation of a mop being k. The main theorem reduces the vertex separation of mops to a special kind of stretchability, one that we call affixability, of submops.