Two-edge-connected (not necessarily spanning) subgraphs and polyhedra
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866916450950709248 |
|---|---|
| author | Bruckamp, Justus Chimani, Markus Juhnke, Martina |
| author_facet | Bruckamp, Justus Chimani, Markus Juhnke, Martina |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_18564 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Two-edge-connected (not necessarily spanning) subgraphs and polyhedra Bruckamp, Justus Chimani, Markus Juhnke, Martina Combinatorics 05C40, 05C45, 52B12, 52B20, 90C27 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. |
| title | Two-edge-connected (not necessarily spanning) subgraphs and polyhedra |
| topic | Combinatorics 05C40, 05C45, 52B12, 52B20, 90C27 |
| url | https://arxiv.org/abs/2410.18564 |