# On the Dominant of the Multicut Polytope

@article{Chimani2021OnTD, title={On the Dominant of the Multicut Polytope}, author={Markus Chimani and Martina Juhnke-Kubitzke and Alexander Nover}, journal={ArXiv}, year={2021}, volume={abs/2112.01095} }

Given a graph G = (V,E) and a set S ⊆ ( V 2 ) of terminal pairs, the minimum multicut problem asks for a minimum edge set δ ⊆ E such that there is no s-t-path in G− δ for any {s, t} ∈ S. For |S| = 1 this is the well known s-tcut problem, but in general the minimum multicut problem is NP-complete, even if the input graph is a tree. The multicut polytope MultC (G,S) is the convex hull of all multicuts in G; the multicut dominant is given by MultC(G,S) = MultC (G,S) + RE. The latter is the…

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