Note on Long Directed Cycles in Eulerian Digraphs

Jiangdong Ai; Gregory Gutin; Fankang He; Anders Yeo

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arXiv · 2510.26426

Note on Long Directed Cycles in Eulerian Digraphs

Jiangdong Ai·Gregory Gutin·Fankang He·Anders Yeo

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Abstract

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

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BibTeX RIS

Jiangdong Ai, Gregory Gutin, Fankang He, Anders Yeo. 2025-10-30. Note on Long Directed Cycles in Eulerian Digraphs. https://arxiv.org/abs/2510.26426

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