On contracting hyperplane elements from a 3-connected matroid

Details On contracting hyperplane elements from a 3-connected matroid On contracting hyperplane elements from a 3-connected matroid

2008-02-25

arxiv.org/abs/0802.3527v1

Mathematics

Combinatorics

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

Scientific paper

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.

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