1 research outputs found
Maximum cuts in edge-colored graphs
The input of the Maximum Colored Cut problem consists of a graph
with an edge-coloring and a positive integer ,
and the question is whether has a nontrivial edge cut using at least
colors. The Colorful Cut problem has the same input but asks for a nontrivial
edge cut using all 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 . On the positive side, we
prove that Maximum Colored Cut is fixed-parameter tractable when parameterized
by either or , by constructing a cubic kernel in both cases.Comment: 15 pages, 6 figure