# On nonbinary 3-connected matroids

@article{Oxley1987OnN3, title={On nonbinary 3-connected matroids}, author={James G. Oxley}, journal={Transactions of the American Mathematical Society}, year={1987}, volume={300}, pages={663-679} }

It is well known that a matroid is binary if and only if it has no minor isomorphic to U2,4, the 4-point line. Extending this result, Bixby proved that every element in a nonbinary connected matroid is in a U2,4minor. The result was further extended by Seymour who showed that every pair of elements in a nonbinary 3-connected matroid is in a U2,4-minor. This paper extends Seymour's theorem by proving that if {x, y, z} is contained in a nonbinary 3-connected matroid M, then either M has a U2,4…

## 46 Citations

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We show that a matroid is binary or ternary if and only if it has no minor isomorphic to U2,5, U3,5, U2,4 ⊕ F7, U2,4 ⊕ F ∗ 7 , U2,4 ⊕2 F7, U2,4 ⊕2 F ∗ 7 , or the unique matroids obtained by relaxing…

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