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- W2000704782 abstract "Tutte proved that if e is an element of a 3-connected matroid M such that neither Me nor M/e is 3-connected, then e is in a 3-circuit or a 3-cocircuit. In this paper, we prove a broad generalization of this result. Among the consequences of this generalization are that if X is an ( n − 1)-element subset of an n-connected matroid M such that neither MX nor M/X is connected, then, provided | E ( M )| ≥ 2( n − 1)≥ 4, X is in both an n -element circuit and an n -element cocircuit. When n = 3, we describe the structure of M more closely using Δ − Y exchanges. Several related results are proved and we also show that, for all fields F other than GF (2), the set of excluded minors for F -representability is closed under both Δ − Y and Y − Δ exchanges." @default.
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- W2000704782 date "1993-12-01" @default.
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- W2000704782 title "Some Local Extremal Connectivity Results for Matroids" @default.
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- W2000704782 doi "https://doi.org/10.1017/s0963548300000766" @default.
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