Every Minor-Closed Property of Sparse Graphs is Testable
| dc.creator | Benjamini, Itai | |
| dc.creator | Schramm, Oded | |
| dc.creator | Shapira, Asaf | |
| dc.date | 2008-01-18 | |
| dc.date | 2008-02-10 | |
| dc.date.accessioned | 2026-07-07T09:19:25Z | |
| dc.date.available | 2026-07-07T09:19:25Z | |
| dc.description | Suppose $G$ is a graph with degrees bounded by $d$, and one needs to remove more than $εn$ of its edges in order to make it planar. We show that in this case the statistics of local neighborhoods around vertices of $G$ is far from the statistics of local neighborhoods around vertices of any planar graph $G'$ with the same degree bound. In fact, a similar result is proved for any minor-closed property of bounded degree graphs. As an immediate corollary of the above result we infer that many well studied graph properties, like being planar, outer-planar, series-parallel, bounded genus, bounded tree-width and several others, are testable with a constant number of queries, where the constant may depend on $ε$ and $d$, but not on the graph size. None of these properties was previously known to be testable even with $o(n)$ queries. | |
| dc.identifier | https://arxiv.org/abs/0801.2797 | |
| dc.identifier | http://arxiv.org/abs/0801.2797 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/154385 | |
| dc.subject | Combinatorics | |
| dc.subject | Probability | |
| dc.subject | 05C10; 05C83; 68R10 | |
| dc.title | Every Minor-Closed Property of Sparse Graphs is Testable | |
| dc.type | text |