Abstract
In 2012, Henning and Yeo have posed the conjecture that a bipartite 3-regular digraph contains two disjoint cycles of different lengths, and Tan has proved that a 3-regular bipartite digraph, which possesses a cycle factor with at least two cycles, does indeed have two disjoint cycles of different lengths. In this paper, we prove that every 3-regular digraph, which possesses a cycle factor with at least three cycles, contains two disjoint cycles of different lengths, except for the digraph that is isomorphic to the \(D_{2n}^2\) (\(n\ge 3\)).
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Acknowledgements
We would like to thank the anonymous reviewers for their valuable comments and corrections.
Funding
This work is supported by the National Natural Science Foundation of China (Nos. 12171414 and 12061056) and the Ningxia Natural Science Foundation (No. 2021AAC05001).
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This work is supported by the National Natural Science Foundation of China (Nos. 12171414 and 12061056) and the Ningxia Natural Science Foundation (No. 2021AAC05001).
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He, Z., Cheng, P. & Gao, Y. Disjoint Cycles of Different Lengths in 3-Regular Digraphs. Graphs and Combinatorics 38, 74 (2022). https://doi.org/10.1007/s00373-022-02465-3
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DOI: https://doi.org/10.1007/s00373-022-02465-3