# On chains of 3-connected matroids

@article{Bixby1986OnCO,
title={On chains of 3-connected matroids},
author={Robert E. Bixby and Collette R. Coullard},
journal={Discret. Appl. Math.},
year={1986},
volume={15},
pages={155-166}
}
• Published 1 November 1986
• Mathematics
• Discret. Appl. Math.
10 Citations
On the Structure of 3-connected Matroids and Graphs
• Mathematics
Eur. J. Comb.
• 2000
It is proved that the essential elements of M can be partitioned into classes where two elements are in the same class if M has a fan, a maximal partial wheel, containing both and if an essential element e of M is in more than one fan, then that fan has three or five elements.
Vertically N-contractible elements in 3-connected matroids
In this paper we establish a variation of the Splitter Theorem. Let $M$ and $N$ be simple 3-connected matroids. We say that $x\in E(M)$ is vertically $N$-contractible if $si(M/x)$ is a 3-connected
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.
Linearly Synthesizing 2-Connected Simplicial Graphs
• Mathematics
• 1995
It is proved that for any two 2-connected, smooth, and simplicial graphs G and H such that H is homeomorphic to a subgraph of G, there is a sequence of 2-connected subgraphs G0 I G1 I. . . I Gr = G
Extensions of Tutte's wheels-and-whirls theorem
• Mathematics
J. Comb. Theory, Ser. B
• 1992
Extensions of Tutte's
• Mathematics
• 1992

## References

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Connectivity in Matroids
• W. T. Tutte
• Mathematics