### Abstract

Original language | English |
---|---|

Title of host publication | Proc. $34^th$ European Workshop on Computational Geometry EuroCG '18 |

Place of Publication | Berlin, Germany |

Pages | 32:1-32:6 |

Publication status | Published - 2018 |

### Cite this

*Proc. $34^th$ European Workshop on Computational Geometry EuroCG '18*(pp. 32:1-32:6). Berlin, Germany.

**NP-Completeness of Max-Cut for Segment Intersection Graphs.** / Aichholzer, Oswin; Mulzer, Wolfgang; Schnider, Partick; Vogtenhuber, Birgit.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Research › peer-review

*Proc. $34^th$ European Workshop on Computational Geometry EuroCG '18.*Berlin, Germany, pp. 32:1-32:6.

}

TY - GEN

T1 - NP-Completeness of Max-Cut for Segment Intersection Graphs

AU - Aichholzer, Oswin

AU - Mulzer, Wolfgang

AU - Schnider, Partick

AU - Vogtenhuber, Birgit

PY - 2018

Y1 - 2018

N2 - We consider the problem of finding a maximum cut in a graph $G = (V, E)$, that is, a partition $ V_1 dotcup V_2$ of $V$ such that the number of edges between $V_1$ and $V_2$ is maximum. It is well known that the decision problem whether $G$ has a cut of at least a given size is in general NP-complete. We show that this problem remains hard when restricting the input to segment intersection graphs. These are graphs whose vertices can be drawn as straight-line segments, where two vertices share an edge if and only if the corresponding segments intersect. We obtain our result by a reduction from a variant of Planar Max-2-SAT that we introduce and also show to be NP-complete.

AB - We consider the problem of finding a maximum cut in a graph $G = (V, E)$, that is, a partition $ V_1 dotcup V_2$ of $V$ such that the number of edges between $V_1$ and $V_2$ is maximum. It is well known that the decision problem whether $G$ has a cut of at least a given size is in general NP-complete. We show that this problem remains hard when restricting the input to segment intersection graphs. These are graphs whose vertices can be drawn as straight-line segments, where two vertices share an edge if and only if the corresponding segments intersect. We obtain our result by a reduction from a variant of Planar Max-2-SAT that we introduce and also show to be NP-complete.

M3 - Conference contribution

SP - 32:1-32:6

BT - Proc. $34^th$ European Workshop on Computational Geometry EuroCG '18

CY - Berlin, Germany

ER -