In new progress on conjectures of Stein, and Addario-Berry, Havet, Linhares Sales, Reed and Thomassé, we prove that every oriented graph with all in- and out-degrees greater than 5k/8 contains an alternating path of length k. This improves on previous results of Klimošová and Stein, and Chen, Hou and Zhou.
@article{10_37236_13084,
author = {Jozef Skokan and Mykhaylo Tyomkyn},
title = {Alternating paths in oriented graphs with large semidegree},
journal = {The electronic journal of combinatorics},
year = {2025},
volume = {32},
number = {4},
doi = {10.37236/13084},
zbl = {8120117},
url = {http://geodesic.mathdoc.fr/articles/10.37236/13084/}
}
TY - JOUR
AU - Jozef Skokan
AU - Mykhaylo Tyomkyn
TI - Alternating paths in oriented graphs with large semidegree
JO - The electronic journal of combinatorics
PY - 2025
VL - 32
IS - 4
UR - http://geodesic.mathdoc.fr/articles/10.37236/13084/
DO - 10.37236/13084
ID - 10_37236_13084
ER -
%0 Journal Article
%A Jozef Skokan
%A Mykhaylo Tyomkyn
%T Alternating paths in oriented graphs with large semidegree
%J The electronic journal of combinatorics
%D 2025
%V 32
%N 4
%U http://geodesic.mathdoc.fr/articles/10.37236/13084/
%R 10.37236/13084
%F 10_37236_13084
Jozef Skokan; Mykhaylo Tyomkyn. Alternating paths in oriented graphs with large semidegree. The electronic journal of combinatorics, Tome 32 (2025) no. 4. doi: 10.37236/13084
