The maximum removable matching conjecture in k-connected graphs

Let GG be a kk-connected graph on nn vertices with minimum degree δ(G)k+2\delta(G)\ge k+2. A matching is kk-removable when deleting its edges leaves a kk-connected graph. The maximum removable matching conjecture. The graph GG contains a kk-removable matching of size min{n/2,δ(G)}\min\{\lfloor n/2\rfloor,\delta(G)\}. This conjecture concerns the largest matching size permitted by the order of the graph and the minimum-degree bound. The supplied context gives no resolution or partial status for it, so it remains open.

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Primary source

Hengzhe Li, Mingming Zhou, Shinya Fujita and Yaping Mao, “From Halin's Edge Removability to Matching Removability in k-Connected Graphs”, arXiv:2605.24035 (2026).

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