### Abstract

We study the boundary of tractability for the max-cut problem in graphs. Our main result shows that max-cut parameterized above the edwards-erdos bound is fixed-parameter tractable: we give an algorithm that for any connected graph with n vertices and m edges finds a cut of size $$ \frac{m}{2} + \frac{n-1}{4} + k $$ in time 2 o(k)·n 4, or decides that no such cut exists.this answers a long-standing open question from parameterized complexity that has been posed a number of times over the past 15 years.our algorithm has asymptotically optimal running time, under the exponential time hypothesis, and is strengthened by a polynomial-time computable kernel of polynomial size.

Original language | English |
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Pages (from-to) | 734-757 |

Journal | Algorithmica |

Volume | 72 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2015 |

Externally published | Yes |

## Cite this

Crowston, R., Jones, M., & Mnich, M. (2015). Max-Cut parameterized above the Edwards-Erdős bound.

*Algorithmica*,*72*(3), 734-757. https://doi.org/10.1007/s00453-014-9870-z