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Enumerative combinatorics, graph theory, order theory, posets, matroids, designs and other discrete structures. It also includes algebraic, analytic and probabilistic combinatorics.

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Is it known whether Minimum Cost Multicut is APX-hard?

My questions is concerned with the following problem: Given an undirected graph $G = (V, E)$ and (edge costs) $c \in \mathbb{Z}^E$, $$\min \left\{ \sum_{e \in E} c_e x_e\ \middle|\ x \in \{0,1\}^E \ \ …
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Is it known whether Minimum Cost Multicut is APX-hard?

Yes, it is APX-hard. A proof by Demaine et al. is published here.
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