Abstract
A square 1-factorization of a graph is a 1-factorization in which the union of any two distinct 1-factors is a disjoint union of 4-cycles. We show that a graph admits a square 1-factorization if and only if it is a Cayley graph with group (ℤ2)n for somen. The rest of the title follows since Cayley graphs of abelian groups are known to be hamiltonian.
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Alspach, B., Bermond, J.-C., Sotteau, D.: Decomposition into Cycles I: Hamiltonian Decompositions in Cycles and Rays, ed. Hahn, G., Sabidussi, G. and Woodrow, R.„ Kluwer Academic Publishers (1990)
Babai, L., Frankl, P., Koller, J., Sabidussi, G.: Hamiltonian Cubic Graphs and Centralizers of Involutions. Canad. J. Math.31, 458–464 (1979)
Cameron, P.: Parallelisms of Complete Designs, London Math. Soc. Lecture Notes23 (1976)
Duffus, D., Kierstead, H., Snevily, H.: An Explicit 1-Factorization in the Middle of the Boolean Lattice, J. Comb. Theory Ser. A65, 334 (1994)
Klerlein, J.: Hamiltonian Cycles in Cayley Color Graphs, J. Graph Theory2, 65–68 (1978)
Kobayashi, M. and Nakamura, G.: On 4-Semiregular 1-Factorizations of Complete Graphs and Complete Bipartite Graphs, J. Graphs and Comb.10, 53–59 (1994)
Tutte, W.: Graph Theory, Addison-Wesley, (1984)
White, A.: Graphs, Groups and Surfaces, North-Holland (1985)
Witte, D.: On Hamiltonian Circuits in Cayley Diagrams, Discrete Math.38, 99–108 (1982)
Witte, D. and Gallian, J.: A survey: Hamiltonian cycles in Cayley Graphs, Discrete Math.51, 293–304 (1984)
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Ihrig, E. Graphs that admit square 1-factorizations are hamiltonian Cayley graphs. Graphs and Combinatorics 11, 319–326 (1995). https://doi.org/10.1007/BF01787812
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DOI: https://doi.org/10.1007/BF01787812