Vertically Ncontractible elements in 3connected matroids
Abstract
In this paper we establish a variation of the Splitter Theorem. Let $M$ and $N$ be simple 3connected matroids. We say that $x\in E(M)$ is vertically $N$contractible if $si(M/x)$ is a 3connected matroid with an $N$minor. Whittle (for $k=1,2$) and Costalonga(for $k=3$) proved that, if $r(M) r(N)\ge k$, then $M$ has a $k$independent set $I$ of vertically $N$contractible elements. Costalonga also characterized an obstruction for the existence of such a 4independent set $I$ in the binary case, provided $r(M)r(N)\ge 5$, and improved this result when $r(M)r(N)\ge 6$, and in the graphic case. In this paper we generalize the results of Costalonga to the nonbinary case. Moreover, we apply our results to the study of properties similar to 3roundedness in classes of matroids.
 Publication:

arXiv eprints
 Pub Date:
 September 2012
 arXiv:
 arXiv:1210.0023
 Bibcode:
 2012arXiv1210.0023C
 Keywords:

 Mathematics  Combinatorics
 EPrint:
 This paper has been withdrawn by the author because it's results are obsolete (the more general results are on a more recent work:arXiv:1405.6454) and still has many minor, being not worth to correct due to obsolescence