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Removable matchings in $2$-connected graphs
A matching $M$ of a $2$-connected graph $G$ is removable if $G-M$ is $2$-connected, extending Halin's classical notion of a removable edge. We prove that for every integer $d\ge 5$, every $2$-connected graph $G$ with $δ(G)\ge d$ and $|V(G)|\ge 2d$ has a removable $d$-matching. This is best possible,
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