Note on Long Directed Cycles in Eulerian Digraphs
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866917050379665408 |
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| author | Ai, Jiangdong Gutin, Gregory He, Fankang Yeo, Anders |
| author_facet | Ai, Jiangdong Gutin, Gregory He, Fankang Yeo, Anders |
| contents | 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 $\sqrt{2d}-3/2.$ |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_26426 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Note on Long Directed Cycles in Eulerian Digraphs Ai, Jiangdong Gutin, Gregory He, Fankang Yeo, Anders Combinatorics 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 $\sqrt{2d}-3/2.$ |
| title | Note on Long Directed Cycles in Eulerian Digraphs |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2510.26426 |