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Euler Tours in Hypergraphs

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Abstract

We show that a quasirandom k-uniform hypergraph G has a tight Euler tour subject to the necessary condition that k divides all vertex degrees. The case when G is complete confirms a conjecture of Chung, Diaconis and Graham from 1989 on the existence of universal cycles for the k-subsets of an n-set.

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Author information

Authors and Affiliations

  1. Institute for Theoretical Studies, ETH Zrich, 8092, Zrich, Switzerland

    Stefan Glock

  2. Institute for Computer Science, Heidelberg University, Heidelberg, Germany

    Felix Joos

  3. School of Mathematics, University of Birmingham, Edgbaston, Birmingham, B15 2TT, UK

    Daniela Kühn & Deryk Osthus

Authors
  1. Stefan Glock
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  2. Felix Joos
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  3. Daniela Kühn
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  4. Deryk Osthus
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Corresponding author

Correspondence to Deryk Osthus.

Additional information

The research leading to these results was partially supported by the European Research Council under the European Union’s Seventh Framework Programme (FP/2007-2013) / ERC Grant 306349 (S. Glock and D. Osthus), and by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) - 339933727 (F. Joos). The research was also partially supported by the EPSRC, grant no. EP/N019504/1, and by the Royal Society and the Wolfson Foundation (D. Kühn).

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Glock, S., Joos, F., Kühn, D. et al. Euler Tours in Hypergraphs. Combinatorica 40, 679–690 (2020). https://doi.org/10.1007/s00493-020-4046-8

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  • DOI: https://doi.org/10.1007/s00493-020-4046-8

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