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- W2913888525 abstract "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 [9] 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 $mathcal{S}_{8}$ 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 $mathcal{S}_{8}$ is the only minor-minimal binary non-balanced matroid, as claimed in [9]. We also give an example of a balanced matroid which is not Rayleigh." @default.
- W2913888525 created "2019-02-21" @default.
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- W2913888525 date "2006-07-31" @default.
- W2913888525 modified "2023-09-25" @default.
- W2913888525 title "Rayleigh Matroids" @default.
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- W2913888525 doi "https://doi.org/10.1017/s0963548306007541" @default.
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