Abstract
We study max-cut in classes of graphs defined by forbidding a single graph as a subgraph, induced subgraph, or minor. For the first two containment relations, we prove dichotomy theorems. For the minor order, we show how to solve max-cut in polynomial time for the class obtained by forbidding a graph with crossing number at most one (this generalizes a known result for K 5-minor-free graphs) and identify an open problem which is the missing case for a dichotomy theorem.
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Kamiński, M. (2010). max-cut and Containment Relations in Graphs. In: Thilikos, D.M. (eds) Graph Theoretic Concepts in Computer Science. WG 2010. Lecture Notes in Computer Science, vol 6410. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-16926-7_4
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DOI: https://doi.org/10.1007/978-3-642-16926-7_4
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