Connected matroids with a small circumference (Q1861209)
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scientific article; zbMATH DE number 1882146
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Connected matroids with a small circumference |
scientific article; zbMATH DE number 1882146 |
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Connected matroids with a small circumference (English)
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16 March 2003
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By a result of Lemos and Oxley a connected matroid \(M\) with \(|E(M)|\geq 3r(M)\) has a circuit \(C\) such that \(M\setminus C\) is connected. The author shows that replacing \(3r(M)\) by \(3r(M)-1\) yields a sharp lower bound. Also, it is shown that \(|E(M)|\geq 3r(M)-3\) whenever \(M\) is simple, connected, and of rank at least 7.
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connected matroid
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circumference
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