Matchings Extend into 2-Factors in Hypercubes


Vandenbussche and West conjectured that every matching of the hypercube can be extended to a 2-factor. We prove this conjecture.

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  1. [1]

    A. Alahmadi, R. E. L. Aldred, A. Alkenani, R. Hijazi, P. Solé and C. Thomassen: Extending a perfect matching to a hamiltonian cycle, Discrete Math-ematics & Theoretical Computer Science 17, 2015.

  2. [2]

    D. Dimitrov, T. Dvořák, P. Gregor and R. Škrekovski: Gray codes avoiding matchings, Discrete Mathematics & Theoretical Computer Science 11 (2009), 123–147.

    MathSciNet  MATH  Google Scholar 

  3. [3]

    T. Dvořák: Hamiltonian cycles with prescribed edges in hypercubes, SIAM J. Dis-cret. Math. 19 (2005), 135–144.

    MathSciNet  MATH  Google Scholar 

  4. [4]

    J. Fink: Perfect matchings extend to Hamilton cycles in hypercubes, J. Comb. The-ory, Ser. B 97 (2007), 1074–1076.

    MathSciNet  Article  MATH  Google Scholar 

  5. [5]

    P. Gregor: Perfect matchings extending on subcubes to Hamiltonian cycles of hypercubes, Discrete Mathematics 309 (2009), 1711–1713.

    MathSciNet  Article  MATH  Google Scholar 

  6. [6]

    L. Gros: Théorie du Baguenodier, Aimé Vingtrinier, Lyon, 1872.

    Google Scholar 

  7. [7]

    D. Kőnig: Über graphen und ihre anwendung auf determinantentheorie und mengenlehre, Mathematische Annalen 77 (1916), 453–465.

    MathSciNet  Article  MATH  Google Scholar 

  8. [8]

    D. E. Knuth: The Art of Computer Programming, Volume 4, Fascicles 0-4, Addison-Wesley Professional, 2009.

    Google Scholar 

  9. [9]

    G. Kreweras: Matchings and Hamiltonian cycles on hypercubes, Bull. Inst. Com-bin. Appl. 16 (1996), 87–91.

    MathSciNet  MATH  Google Scholar 

  10. [10]

    F. Ruskey and C.D. Savage: Hamilton Cycles that Extend Transposition Matchings in Cayley Graphs of Sn, SIAM Journal on Discrete Mathematics 6 (1993), 152–166.

    MathSciNet  Article  MATH  Google Scholar 

  11. [11]

    C. Savage: A survey of combinatorial Gray codes, SIAM Review 39 (1997), 605–629.

    MathSciNet  Article  MATH  Google Scholar 

  12. [12]

    J. Vandenbussche and D. B. West: Extensions to 2-factors in bipartite graphs, The Electronic Journal of Combinatorics 20 (2013), 1–10.

    MathSciNet  MATH  Google Scholar 

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Correspondence to Jiří Fink.

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Supported by the Czech Science Foundation grant GA14-10799S.

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Fink, J. Matchings Extend into 2-Factors in Hypercubes. Combinatorica 39, 77–84 (2019).

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Mathematics Subject Classification (2010)

  • 52C38
  • 05C70
  • 05C65