Abstract
Vandenbussche and West conjectured that every matching of the hypercube can be extended to a 2-factor. We prove this conjecture.
Similar content being viewed by others
References
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.
D. Dimitrov, T. Dvořák, P. Gregor and R. Škrekovski: Gray codes avoiding matchings, Discrete Mathematics & Theoretical Computer Science 11 (2009), 123–147.
T. Dvořák: Hamiltonian cycles with prescribed edges in hypercubes, SIAM J. Dis-cret. Math. 19 (2005), 135–144.
J. Fink: Perfect matchings extend to Hamilton cycles in hypercubes, J. Comb. The-ory, Ser. B 97 (2007), 1074–1076.
P. Gregor: Perfect matchings extending on subcubes to Hamiltonian cycles of hypercubes, Discrete Mathematics 309 (2009), 1711–1713.
L. Gros: Théorie du Baguenodier, Aimé Vingtrinier, Lyon, 1872.
D. Kőnig: Über graphen und ihre anwendung auf determinantentheorie und mengenlehre, Mathematische Annalen 77 (1916), 453–465.
D. E. Knuth: The Art of Computer Programming, Volume 4, Fascicles 0-4, Addison-Wesley Professional, 2009.
G. Kreweras: Matchings and Hamiltonian cycles on hypercubes, Bull. Inst. Com-bin. Appl. 16 (1996), 87–91.
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.
C. Savage: A survey of combinatorial Gray codes, SIAM Review 39 (1997), 605–629.
J. Vandenbussche and D. B. West: Extensions to 2-factors in bipartite graphs, The Electronic Journal of Combinatorics 20 (2013), 1–10.
Author information
Authors and Affiliations
Corresponding author
Additional information
Supported by the Czech Science Foundation grant GA14-10799S.