### Abstract

Spectral graph bisections are a popular heuristic aimed at approximating the solution of the NP-complete graph bisection problem. This technique, however, does not always provide a robust tool for graph partitioning. Using a special class of graphs, we prove that the standard spectral graph bisection can produce bisections that are far from optimal. In particular, we show that the maximum error in the spectral approximation of the optimal bisection (partition sizes exactly equal) cut for such graphs is bounded below by a constant multiple of the order of the graph squared.

Original language | English (US) |
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Pages (from-to) | 1972-1979 |

Number of pages | 8 |

Journal | Linear and Multilinear Algebra |

Volume | 64 |

Issue number | 10 |

DOIs | |

State | Published - Oct 2 2016 |

### All Science Journal Classification (ASJC) codes

- Algebra and Number Theory

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## Cite this

Urschel, J. C., & Zikatanov, L. T. (2016). On the maximal error of spectral approximation of graph bisection.

*Linear and Multilinear Algebra*,*64*(10), 1972-1979. https://doi.org/10.1080/03081087.2015.1133557