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# Karl Däubel

**Research assistant**

Fakultät II - Mathematik und Naturwissenschaften

Institut für Mathematik, Sekr. MA 5-2

Technische Universität Berlin

Straße des 17. Juni 136

10623 Berlin

Germany

E-Mail: daeubel #at# math.tu-berlin.de

Tel.: +49 (0)30 314-78657

Fax: +49 (0)30 314-25191

Room: MA 514

Office hour: by appointment

## Research Interests

Combinatorial optimization and algorithms:

- unsplittable flows/Ring Loading
- applications in logistics for large scale networks
- incremental flows

## Publications

Citation key | DaeubelJaegerMuetzeScheucher2019 |
---|---|

Author | Däubel, Karl and Jäger, Sven and Mütze, Torsten and Scheucher, Manfred |

Title of Book | Proceedings of the European Conference on Combinatorics, Graph Theory and Applications (EUROCOMB) |

Pages | 611–618 |

Year | 2019 |

ISSN | 0862-9544 |

Location | Bratislava |

Journal | Acta Mathematica Universitatis Comenianae |

Volume | 88 |

Number | 3 |

Month | August |

Note | extended abstract |

Editor | Nešetřil, Jaroslav and Škoviera, Martin |

Abstract | The n-cube is the poset obtained by ordering all subsets of 1,...,n by inclusion, and it can be partitioned into n choose ⌊n/2⌋ chains, which is the minimum possible number. Two such decompositions of the n-cube are called orthogonal if any two chains of the decomposition share at most a single element. Shearer and Kleitman conjectured in 1979 that the n-cube has ⌊n/2⌋+1 pairwise orthogonal decompositions into the minimum possible number of chains, and they constructed two such decompositions. Spink recently improved this by showing that the n-cube has three pairwise orthogonal chain decompositions for n ≥ 24. In this paper, we construct four pairwise orthogonal chain decompositions of the n-cube for n ≥ 60. We also construct five pairwise edge-disjoint symmetric chain decompositions of the n-cube for n ≥ 90, where edge-disjointness is a slightly weaker notion than orthogonality, improving on a recent result by Gregor, Jäger, Mütze, Sawada, and Wille. |