• Corpus ID: 228375389

On the Bond Polytope

@article{Chimani2020OnTB,
  title={On the Bond Polytope},
  author={Markus Chimani and Martina Juhnke-Kubitzke and Alexander Nover},
  journal={ArXiv},
  year={2020},
  volume={abs/2012.06288}
}
Given a graph $G=(V,E)$, the maximum bond problem searches for a maximum cut $\delta(S) \subseteq E$ with $S \subseteq V$ such that $G[S]$ and $G[V\setminus S]$ are connected. This problem is closely related to the well-known maximum cut problem and known under a variety of names such as largest bond, maximum minimal cut and maximum connected (sides) cut. The bond polytope is the convex hull of all incidence vectors of bonds. Similar to the connection of the corresponding optimization problems… 

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References

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TLDR
It is shown that {\sc Largest Bond} remains NP-hard even for planar bipartite graphs, and it does not admit a constant-factor approximation algorithm, unless $P = NP, and both problems are fixed-parameter tractable when parameterized by the size of the solution, but they do not admit polynomial kernels unless NP $\subseteq coNP/poly.
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TLDR
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TLDR
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TLDR
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TLDR
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