On contracting hyperplane elements from a 3-connected matroid

Abstract

Let ${\tilde{K}}_{3,n}$, $n\ge 3$, 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 $M\ncong M^{\ast }({\tilde{K}}_{3,n})$, then there is an element $x$ in $H$ such that the simple matroid associated with $M/x$ is 3-connected.

19 pages, 3 figures, submitted to Advances in Applied Mathematics

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