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Faster Minimum k-Cut I: Simple and Sparse Weighted Graphs
The minimum $k$-cut problem asks for the fewest edges whose removal leaves an input graph with at least $k$ connected components. Previously, the best algorithm for simple graphs ran in $O_k(n^{(1-\varepsilon)k+O(1)})$ time~\cite{HL22}, showing that the \(n^k\) barrier can be broken up to a polynomi
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