English

Note on Long Directed Cycles in Eulerian Digraphs

Combinatorics 2025-10-31 v1

Abstract

Huang, Ma, Shapira, Sudakov and Yuster (Comb. Prob. Comput. 2013) proved that every Eulerian digraph of average out-degree dd has a directed cycle of length at least d.\sqrt{d}. We improve the lower bound from d\sqrt{d} to 2d3/2.\sqrt{2d}-3/2.

Keywords

Cite

@article{arxiv.2510.26426,
  title  = {Note on Long Directed Cycles in Eulerian Digraphs},
  author = {Jiangdong Ai and Gregory Gutin and Fankang He and Anders Yeo},
  journal= {arXiv preprint arXiv:2510.26426},
  year   = {2025}
}

Comments

4 pages

R2 v1 2026-07-01T07:13:43.094Z