Rayleigh Matroids
| dc.creator | Choe, Y. -B. | |
| dc.creator | Wagner, D. G. | |
| dc.date | 2003-07-08 | |
| dc.date | 2003-09-05 | |
| dc.date.accessioned | 2026-07-07T04:59:29Z | |
| dc.date.available | 2026-07-07T04:59:29Z | |
| dc.description | Motivated by a property of linear resistive electrical networks, we introduce the class of Rayleigh matroids. This is a subclass of the balanced matroids introduced by Feder and Mihail [FM] in 1992. We prove a variety of results relating Rayleigh matroids to other well-known classes -- in particular, we show that a binary matroid is Rayleigh if and only if it does not contain S_8 as a minor. This has the consequence that a binary matroid is balanced if and only if it is Rayleigh, and provides the first complete proof in print that S_8 is the only minor-minimal binary non-balanced matroid, as claimed in [FM]. We also give an example of a balanced matroid which is not Rayleigh. | |
| dc.description | 22 pages | |
| dc.identifier | https://arxiv.org/abs/math/0307096 | |
| dc.identifier | http://arxiv.org/abs/math/0307096 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/68002 | |
| dc.subject | Combinatorics | |
| dc.subject | 05B35; 05A20, 05A15, 94C05 | |
| dc.title | Rayleigh Matroids | |
| dc.type | text |