Advertisement

Matchings Extend into 2-Factors in Hypercubes

  • Jiří Fink
Article

Abstract

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

Mathematics Subject Classification (2010)

52C38 05C70 05C65 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  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.Google Scholar
  2. [2]
    D. Dimitrov, T. Dvořák, P. Gregor and R. Škrekovski: Gray codes avoiding matchings, Discrete Mathematics & Theoretical Computer Science 11 (2009), 123–147.MathSciNetMATHGoogle Scholar
  3. [3]
    T. Dvořák: Hamiltonian cycles with prescribed edges in hypercubes, SIAM J. Dis-cret. Math. 19 (2005), 135–144.MathSciNetMATHGoogle Scholar
  4. [4]
    J. Fink: Perfect matchings extend to Hamilton cycles in hypercubes, J. Comb. The-ory, Ser. B 97 (2007), 1074–1076.MathSciNetCrossRefMATHGoogle Scholar
  5. [5]
    P. Gregor: Perfect matchings extending on subcubes to Hamiltonian cycles of hypercubes, Discrete Mathematics 309 (2009), 1711–1713.MathSciNetCrossRefMATHGoogle 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.MathSciNetCrossRefMATHGoogle 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.MathSciNetMATHGoogle 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.MathSciNetCrossRefMATHGoogle Scholar
  11. [11]
    C. Savage: A survey of combinatorial Gray codes, SIAM Review 39 (1997), 605–629.MathSciNetCrossRefMATHGoogle 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.MathSciNetMATHGoogle Scholar

Copyright information

© János Bolyai Mathematical Society and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Theoretical Computer Science and Mathematical Logic Faculty of Mathematics and PhysicsCharles University in PraguePragueCzech Republic

Personalised recommendations