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Karl DäubelKarl Däubel

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Karl Däubel

Lupe

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:
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

On orthogonal symmetric chain decompositions
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.
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