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.
@article{10_37236_10297,
author = {Charlotte Knierim and Maxime Larcher and Anders Martinsson},
title = {Note on long paths in {Eulerian} digraphs},
journal = {The electronic journal of combinatorics},
year = {2021},
volume = {28},
number = {2},
doi = {10.37236/10297},
zbl = {1466.05082},
url = {http://geodesic.mathdoc.fr/articles/10.37236/10297/}
}
TY - JOUR
AU - Charlotte Knierim
AU - Maxime Larcher
AU - Anders Martinsson
TI - Note on long paths in Eulerian digraphs
JO - The electronic journal of combinatorics
PY - 2021
VL - 28
IS - 2
UR - http://geodesic.mathdoc.fr/articles/10.37236/10297/
DO - 10.37236/10297
ID - 10_37236_10297
ER -
%0 Journal Article
%A Charlotte Knierim
%A Maxime Larcher
%A Anders Martinsson
%T Note on long paths in Eulerian digraphs
%J The electronic journal of combinatorics
%D 2021
%V 28
%N 2
%U http://geodesic.mathdoc.fr/articles/10.37236/10297/
%R 10.37236/10297
%F 10_37236_10297
Charlotte Knierim; Maxime Larcher; Anders Martinsson. Note on long paths in Eulerian digraphs. The electronic journal of combinatorics, Tome 28 (2021) no. 2. doi: 10.37236/10297
