Note on Long Paths in Eulerian Digraphs

Charlotte Knierim; Maxime Larcher; Anders Martinsson

Note on Long Paths in Eulerian Digraphs

Combinatorics 2021-10-20 v2

Authors: Charlotte Knierim , Maxime Larcher , Anders Martinsson

Abstract

Long Paths and Cycles in eulerian digraphs have gotten a lot of attention recently. In this short note, we show how to use methods from Knierim, Larcher, Martinsson, Noever (2021) to find paths of length $d/(\log d+1)$ in Eulerian digraphs with average degree $d$ , improving the recent result of $\Omega(d^{1/2+1/40})$ . Our result is optimal up to at most a logarithmic factor.

Keywords

dyck paths

Cite

@article{arxiv.2103.05330,
  title  = {Note on Long Paths in Eulerian Digraphs},
  author = {Charlotte Knierim and Maxime Larcher and Anders Martinsson},
  journal= {arXiv preprint arXiv:2103.05330},
  year   = {2021}
}

Comments

4 pages

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