The st-bond polytope on series-parallel graphs

Circuit and bond polytopes on series-parallel graphs

In this paper, we describe the circuit polytope on series-parallel graphs. We first show the existence of a compact extended formulation. Though not being explicit, its construction process helps us to inductively provide the description in the original space. As a consequence, using the link between bonds and circuits in planar graphs, we also describe the bond polytope on series-parallel graphs.

Equistable series-parallel graphs

A graph is called equistable when there is a non-negative weight function on its vertices such that a set S of vertices has total weight 1 if and only if S is maximal stable. We characterize those series-parallel graphs that are equistable, generalizing results of Mahadev, Peled and Sun about equistable outer-planar graphs.

Earliest arrival flows on series-parallel graphs

We present an exact algorithm for computing an earliest arrival flow in a discrete time setting on series-parallel graphs. In contrast to previous results for the earliest arrival flow problem this algorithm runs in polynomial time.

ESP: pursuit evasion on series-parallel graphs

We study pursuit-evasion problems where pursuers have to clear a given graph of fast-moving evaders despite poor visibility, for example, where police search a cave system to ensure that no terrorists are hiding in it. If the vertex connectivity of some part of the graph exceeds the number of pursuers, the evaders can always avoid capture. We therefore focus on graphs whose subgraphs can always...

Drawing series-parallel graphs on a box