%0 Journal Article
%T On contracting hyperplane elements from a 3-connected matroid
%A Rhiannon Hall
%J Mathematics
%D 2008
%I arXiv
%X Let $\tilde{K}_{3,n}$, $n\geq 3$, be the simple graph obtained from $K_{3,n}$ by adding three edges to a vertex part of size three. We prove that if $H$ is a hyperplane of a 3-connected matroid $M$ and $M \not\cong M^*(\tilde{K}_{3,n})$, then there is an element $x$ in $H$ such that the simple matroid associated with $M/x$ is 3-connected.
%U http://arxiv.org/abs/0802.3527v1