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• W2765657952 abstract "The input of the Maximum Colored Cut problem consists of a graph $G=(V,E)$ with an edge-coloring $c:Eto {1,2,3,ldots , p}$ and a positive integer $k$, and the question is whether $G$ has a nontrivial edge cut using at least $k$ colors. The Colorful Cut problem has the same input but asks for a nontrivial edge cut using all $p$ colors. Unlike what happens for the classical Maximum Cut problem, we prove that both problems are NP-complete even on complete, planar, or bounded treewidth graphs. Furthermore, we prove that Colorful Cut is NP-complete even when each color class induces a clique of size at most 3, but is trivially solvable when each color induces a $K_2$. On the positive side, we prove that Maximum Colored Cut is fixed-parameter tractable when parameterized by either $k$ or $p$, by constructing a cubic kernel in both cases." @default.
• W2765657952 created "2017-11-10" @default.
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• W2765657952 date "2018-05-02" @default.
• W2765657952 modified "2023-09-25" @default.
• W2765657952 title "Maximum cuts in edge-colored graphs" @default.
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• W2765657952 hasPublicationYear "2018" @default.
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