Almost Tight Lower Bounds for Hard Cutting Problems in Embedded Graphs

  title={Almost Tight Lower Bounds for Hard Cutting Problems in Embedded Graphs},
  author={Vincent Cohen-Addad and {\'E}ric Colin de Verdi{\`e}re and D{\'a}niel Marx and Arnaud de Mesmay},
We prove essentially tight lower bounds, conditionally to the Exponential Time Hypothesis, for two fundamental but seemingly very different cutting problems on surface-embedded graphs: the Shortest Cut Graph problem and the Multiway Cut problem. A cut graph of a graph G embedded on a surface S is a subgraph of G whose removal from S leaves a disk. We consider the problem of deciding whether an unweighted graph embedded on a surface of genus g has a cut graph of length at most a given value. We… 
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