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Vertex-Disjoint Cycles of Different Lengths in Local Tournaments

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Abstract

We show in this paper that every strong local tournament with minimum out-degree 3, except the digraphs \(D^3_7\) and \(D^3_8\), contains two vertex-disjoint cycles of different lengths.

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References

  1. Abreu, M., Aldred, E.L., Funk, M., Jackson, B., Labbate, D., Sheehan, J.: Graphs and digraphs with all 2-factors isomorphic. J. Combin. Theory Ser. B 92, 395–404 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  2. Bang-Jensen, J., Gutin, G.: Digraphs. Theory, Algorithms and Applications. Springer, New York (2001)

    MATH  Google Scholar 

  3. Bang-Jensen, J., Havet, F.: Tournaments and semicomplete digraphs. In: Bang-Jensen, J., Gutin, G. (eds.) Classes of Directed Graphs, pp. 35–124. Springer, New York (2018)

    Chapter  Google Scholar 

  4. Bensmail, J., Harutyunyan, A., Le, N.K., Li, B., Lichiardopol, N.: Disjoint cycles of different lengths in graphs and digraphs. Electron. J. Combin. 24, Article P4.37 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  5. Gao, Y., Ma, D.: Disjoint cycles with different length in 4-arc-dominated digraphs. Oper. Res. Lett. 41, 650–653 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  6. He, Z., Cheng, P., Gao, Y.: Disjoint cycles of different lengths in 3-regular digraphs. Graphs Combin. 38(3), Article 74 (2022)

    Article  MathSciNet  MATH  Google Scholar 

  7. Henning, M.A., Yeo, A.: Vertex disjoint cycles of different length in digraphs. SIAM J. Discrete Math. 26, 687–694 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  8. Hung, L.X., Hieu, D.D., Tan, N.D.: Vertex-disjoint cycles of different lengths in multipartite tournaments. Discrete Math. 345, Article 112819 (2022)

    Article  MathSciNet  MATH  Google Scholar 

  9. Lichiardopol, N.: Proof of a conjecture of Henning and Yeo on vertex-disjoint directed cycles. SIAM J. Discrete Math. 28, 1618–1627 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  10. Steiner, R.M.: Disjoint cycles with length constraints in digraphs of large connectivity or large minimum degree. SIAM J. Discrete Math. 36(2), 1343–1362 (2022)

    Article  MathSciNet  MATH  Google Scholar 

  11. Tan, N.D.: Vertex disjoint cycles of different lengths in \(d\)-arc-dominated digraphs. Oper. Res. Lett. 42, 351–354 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  12. Tan, N.D.: On vertex disjoint cycles of different lengths in 3-regular digraphs. Discrete Math. 338, 2485–2491 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  13. Tan, N.D.: On 3-regular digraphs without vertex disjoint cycles of different lengths. Discrete Math. 340, 1933–1943 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  14. Tan, N.D.: On 3-regular digraphs of girth 4. Discrete Math. 342, Article 111632 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  15. Tan, N.D.: Tournaments and bipartite tournaments without vertex disjoint cycles of different lengths. SIAM J. Discrete Math. 35(1), 485–494 (2021)

    Article  MathSciNet  MATH  Google Scholar 

  16. Tan, N.D.: A decomposition for digraphs with minimum outdegree 3 having no vertex disjoint cycles of different lengths. Discussiones Math. Graph Theory 43, 573–581 (2023)

    Article  MathSciNet  Google Scholar 

  17. Thomassen, C.: Disjoint cycles in digraphs. Combinatorica 3, 393–396 (1983)

    Article  MathSciNet  MATH  Google Scholar 

  18. Yeo, A.: Semicomplete multipartite digraphs. In: Bang-Jensen, J., Gutin, G. (eds.) Classes of Directed Graphs, pp. 297–340. Springer, New York (2018)

    Chapter  Google Scholar 

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Correspondence to Le Xuan Hung.

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Hung, L.X., Tan, N.D. Vertex-Disjoint Cycles of Different Lengths in Local Tournaments. Graphs and Combinatorics 39, 92 (2023). https://doi.org/10.1007/s00373-023-02686-0

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  • DOI: https://doi.org/10.1007/s00373-023-02686-0

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