On the Expansion of Graphs of 0/1-Polytopes
| dc.creator | Kaibel, Volker | |
| dc.date | 2001-12-14 | |
| dc.date.accessioned | 2026-07-07T04:45:15Z | |
| dc.date.available | 2026-07-07T04:45:15Z | |
| dc.description | The edge expansion of a graph is the minimum quotient of the number of edges in a cut and the size of the smaller one among the two node sets separated by the cut. Bounding the edge expansion from below is important for bounding the ``mixing time'' of a random walk on the graph from above. It has been conjectured by Mihail and Vazirani that the graph of every 0/1-polytope has edge expansion at least one. A proof of this (or even a weaker) conjecture would imply solutions of several long-standing open problems in the theory of randomized approximate counting. We present different techniques for bounding the edge expansion of a 0/1-polytope from below. By means of these tools we show that several classes of 0/1-polytopes indeed have graphs with edge expansion at least one. These classes include all 0/1-polytopes of dimension at most five, all simple 0/1-polytopes, all hypersimplices, all stable set polytopes, and all (perfect) matching polytopes. | |
| dc.description | 19 pages | |
| dc.identifier | https://arxiv.org/abs/math/0112146 | |
| dc.identifier | http://arxiv.org/abs/math/0112146 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/62891 | |
| dc.subject | Combinatorics | |
| dc.subject | Probability | |
| dc.subject | 52B12; 52B11; 52B05; 68W20;60G50 | |
| dc.title | On the Expansion of Graphs of 0/1-Polytopes | |
| dc.type | text |