# Branch-Width and Rota's Conjecture

@article{Geelen2002BranchWidthAR, title={Branch-Width and Rota's Conjecture}, author={James F. Geelen and Geoff Whittle}, journal={J. Comb. Theory, Ser. B}, year={2002}, volume={86}, pages={315-330} }

- Published 2002 in J. Comb. Theory, Ser. B
DOI:10.1006/jctb.2002.2130

We begin by giving some background to this result. A matroid M is an excluded minor for a minor-closed class of matroids if M is not in the class but all proper minors of M are. It is natural to attempt to characterize a minor-closed class of matroids by giving a complete list of its excluded minors. Unfortunately, a minor-closed class of matroids can have an infinite number of excluded minors. For example, this is the case for the matroids representable over the rationals; see [7]. Thisâ€¦Â CONTINUE READING

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View 4 Excerpts

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View 1 Excerpt

## Special Issue in Honor of Geoff Whittle

View 1 Excerpt

## On Codes of Bounded Trellis Complexity

View 1 Excerpt

#### References

##### Publications referenced by this paper.

Showing 1-10 of 14 references

## Combinatorial theory, old and new, in â€˜â€˜Proceedings of the International Congress on Mathematics,â€™

View 9 Excerpts

Highly Influenced

## Tutte, Mengerâ€™s theorem for matroids

View 9 Excerpts

Highly Influenced

## Branch-Width and Well-Quasi-Ordering in Matroids and Graphs

View 7 Excerpts

## The Excluded Minors for GF(4)-Representable Matroids

View 1 Excerpt

## Highly Connected Sets and the Excluded Grid Theorem

View 1 Excerpt

## A menger-like property of tree-width: The finite case

View 1 Excerpt

## On forbidden minors for GF Ã°3Ãž

View 1 Excerpt

## Matroid representation over GF(3)

View 1 Excerpt