A Graph Bottleneck Inequality
| dc.creator | Chebotarev, Pavel | |
| dc.date | 2008-10-15 | |
| dc.date | 2009-05-20 | |
| dc.date.accessioned | 2026-07-07T13:16:38Z | |
| dc.date.available | 2026-07-07T13:16:38Z | |
| dc.description | For a weighted directed multigraph, let $f_{ij}$ be the total weight of spanning converging forests that have vertex $i$ in a tree converging to $j$. We prove that $f_{ij} f_{jk} = f_{ik} f_{jj}$ if and only if every directed path from $i$ to $k$ contains $j$ (a graph bottleneck equality). Otherwise, $f_{ij} f_{jk} < f_{ik} f_{jj}$ (a graph bottleneck inequality). In a companion paper (P. Chebotarev, A new family of graph distances, arXiv preprint arXiv:0810.2717}. Submitted), this inequality underlies, by ensuring the triangle inequality, the construction of a new family of graph distances. This stems from the fact that the graph bottleneck inequality is a multiplicative counterpart of the triangle inequality for proximities. | |
| dc.description | 6 pages. A revised version | |
| dc.identifier | https://arxiv.org/abs/0810.2732 | |
| dc.identifier | http://arxiv.org/abs/0810.2732 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/230854 | |
| dc.subject | Combinatorics | |
| dc.subject | 05C50; 05C05; 15A51 | |
| dc.title | A Graph Bottleneck Inequality | |
| dc.type | text |