Cut Polytopes of Minor-free Graphs

Markus Chimani; Martina Juhnke-Kubitzke; Alexander Nover; Tim Römer

Cut Polytopes of Minor-free Graphs

Combinatorics 2019-03-06 v1 Discrete Mathematics

Authors: Markus Chimani , Martina Juhnke-Kubitzke , Alexander Nover , Tim Römer

Abstract

The cut polytope of a graph $G$ is the convex hull of the indicator vectors of all cuts in $G$ and is closely related to the MaxCut problem. We give the facet-description of cut polytopes of $K_{3,3}$ -minor-free graphs and introduce an algorithm solving MaxCut on those graphs, which only requires the running time of planar MaxCut. Moreover, starting a systematic geometric study of cut polytopes, we classify graphs admitting a simple or simplicial cut polytope.

Keywords

cut polytope minor-free graphs maxcut facets graph classification

Cite

@article{arxiv.1903.01817,
  title  = {Cut Polytopes of Minor-free Graphs},
  author = {Markus Chimani and Martina Juhnke-Kubitzke and Alexander Nover and Tim Römer},
  journal= {arXiv preprint arXiv:1903.01817},
  year   = {2019}
}

Comments

15 pages, 2 figures, 1 table

Cut Polytopes of Minor-free Graphs

Abstract

Keywords

Cite

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