Detachable pairs in $3$-connected matroids and simple $3$-connected graphs

Nick Brettell, Charles Semple, Gerry Toft

Let $M$ be a $3$-connected matroid. A pair $\{e,f\}$ in $M$ is detachable if $M\backslash e\backslash f$ or $M/e/f$ is $3$-connected. Williams (2015) proved that if $M$ has a…