## Abstract

An instance of the Connected Maximum Cut problem consists of an undirected graph G = (V,E) and the goal is to find a subset of vertices S ⊆ V that maximizes the number of edges in the cut δ(S) such that the induced graph G[S] is connected. We present the first nontrivial (Formula presented) approximation algorithm for the connected maximum cut problem in general graphs using novel techniques. We then extend our algorithm to an edge weighted case and obtain a poly-logarithmic approximation algorithm. Interestingly, in stark contrast to the classical max-cut problem, we show that the connected maximum cut problem remains NP-hard even on unweighted, planar graphs. On the positive side, we obtain a polynomial time approximation scheme for the connected maximum cut problem on planar graphs and more generally on graphs with bounded genus.

Original language | English |
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Title of host publication | Algorithms – ESA 2015 - 23rd Annual European Symposium, Proceedings |

Editors | Nikhil Bansal, Irene Finocchi |

Publisher | Springer Verlag |

Pages | 693-704 |

Number of pages | 12 |

ISBN (Print) | 9783662483497 |

DOIs | |

State | Published - 2015 |

Externally published | Yes |

Event | 23rd European Symposium on Algorithms, ESA 2015 - Patras, Greece Duration: 14 Sep 2015 → 16 Sep 2015 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 9294 |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 23rd European Symposium on Algorithms, ESA 2015 |
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Country/Territory | Greece |

City | Patras |

Period | 14/09/15 → 16/09/15 |

### Bibliographical note

Publisher Copyright:© Springer-Verlag Berlin Heidelberg 2015.