Rayleigh Matroids

Motivated by a property of linear resistive electrical networks, we introduce the class of Rayleigh matroids. These form a subclass of the balanced matroids defined by Feder and Mihail [10] 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 S8 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 S8 is the only minor–minimal binary non–balanced matroid, as claimed in [10]. We also give an example of a balanced matroid which is not Rayleigh.