Year: 2024
Type: preprint
Abstract: Given a graph $G$, we study the $2$-edge-connected subgraph polytope $\mathrm{TECSP}(G)$, which is given by the convex hull of the incidence vectors of all $2$-edge-connected subgraphs of $G$. We describe the lattice points of this polytope by linear inequalities which provides an ILP-algorithm for finding a $2$-edge-connected subgraph of maximum weight. Furthermore, we characterize when these inequalities define facets of $\mathrm{TECSP}(G)$. We also consider further types of supporting hyperplanes of $\mathrm{TECSP}(G)$ and study when they are facet-defining. Finally, we investigate the efficiency of our considered inequalities practically on some classes of graphs.
Source: arXiv (Cornell University)
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4404306901