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Linear-Time FPT Algorithm for Surface Disjoint Paths via Surface Cutting
We study the \textsc{$k$-Disjoint Paths} problem on a graph embedded on a surface with bounded Euler genus. Given a graph $G$ with $n$ vertices and $k$ vertex pairs embedded on a surface of Euler genus $g$, we present a $2^{O(k^2+g^2)}n$-time algorithm that computes $k$ pairwise vertex-disjoint path
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