# Minors of 3-Connected Matroids

```@article{Seymour1985MinorsO3,
title={Minors of 3-Connected Matroids},
author={Paul D. Seymour},
journal={Eur. J. Comb.},
year={1985},
volume={6},
pages={375-382}
}```
• P. Seymour
• Published 1 December 1985
• Mathematics
• Eur. J. Comb.
Triangles in 3-connected matroids
On fixing elements in matroid minors
• Mathematics
Comb.
• 1989
The aim of this note is to prove that, for all sufficiently largen, the collection of n-element 3-connected matroids having some minor in F is also (3, 1)-rounded.
Finding a small 3-connected minor maintaining a fixed minor and a fixed element
• Mathematics
Comb.
• 1987
This result generalizes a theorem of Truemper and can be used to prove Seymour’s 2-roundedness theorem, as well as a result of Oxley on triples in nonbinary matroids.
THE EXCLUDED MINORS FOR THE MATROIDS THAT ARE BINARY OR TERNARY
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
Counterexamples to conjectures on 4-connected matroids
This paper provides counterexamples to two conjectures of Robertson is that each triple of elements in a 4-connected non-graphic matroid is in some circuit.
On Representable Matroids Having Neither U2,5– Nor U3,5–minors
• Mathematics
• 1995
Consider 3–connected matroids that are neither binary nor ternary and have neither U2,5– nor U3,5–minors: for example, AG(3, 2)′, the matroid obtained by relaxing a circuit-hyperplane of AG(3, 2).
Stabilizers of Classes of Representable Matroids
One of the main theorems of this paper proves that if M is minor-closed and closed under duals, and N is 3- connected, then to show that N is a stabilizer it suffices to check 3-connected matroids in M that are single-element extensions or coextensions of N, or are obtained by a single- element extension followed by asingle-element coextension.

## References

SHOWING 1-6 OF 6 REFERENCES
On minors of non-binary matroids
It is proved that for every two elements of a 3-connected non-binary matroid, there is aU42 minor using them both.