Euler Tours in Hypergraphs

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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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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Mathematics Subject Classification (2010)

  • 05B40
  • 05C45
  • 05C65
  • 05C81