descriptionPublicationkeyboard_double_arrow_right Article , Preprint 18 Jun 2021Embargo end date: 01 Jan 2021Publisher:The Electronic Journal of CombinatoricsJournal:The Electronic Journal of Combinatorics, volume 28 (eissn: 1077-8926,

Authors: Maxime Larcher; Charlotte Knierim; Anders Martinsson;

doi: 10.37236/10297 , 10.48550/arxiv.2103.05330

arXiv: http://arxiv.org/abs/2103.05330

Note on Long Paths in Eulerian Digraphs

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Abstract

Long paths and cycles in Eulerian digraphs have received a lot of attention recently. In this short note, we show how to use methods from [Knierim, Larcher, Martinsson, Noever, JCTB 148:125--148] 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.

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ETH Zurich
Switzerland

Keywords

FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO)

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