Geodesic
Extending pairings to Hamiltonian cycles
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 7 (2010), pp. 115-118.

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Recently J. Fink proved that every $1$-factor of the complete graph on the vertex set of the hypercube $Q_n$ can be extended to a cycle by adding some edges of this hypercube. We prove that, for $n\ge4$, one can remove some edges of $Q_n$ so that the resulting graph still has this property. Also we give upper and lower bounds on the minimum number of edges of a $2n$-vertex graph having this property.
Keywords: $1$-factor, Hamiltonian cycle, Kreweras Conjecture
Mots-clés : hypercube. 
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     author = {D. G. Fon-Der-Flaass},
     title = {Extending pairings to {Hamiltonian} cycles},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {115--118},
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     year = {2010},
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     url = {http://geodesic.mathdoc.fr/item/SEMR_2010_7_a10/}
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D. G. Fon-Der-Flaass. Extending pairings to Hamiltonian cycles. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 7 (2010), pp. 115-118. http://geodesic.mathdoc.fr/item/SEMR_2010_7_a10/

[1] J. Fink, “Perfect matchings extend to Hamilton cycles in hypercubes”, J. Combin. Theory Ser. B, 97 (2007), 1074–1076 | DOI | MR | Zbl