Abstract
In this note we show how 1-factors in the middle two layers of the discrete cube can be used to construct 2-factors in the Odd graph (the Kneser graph of (k − 1)-sets from a (2k − 1)-set). In particular, we use the lexical matchings of Kierstead and Trotter, and the modular matchings of Duffus, Kierstead and Snevily, to give explicit constructions of two different 2-factorisations of the Odd graph.
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References
Biggs, N.: Some odd graph theory, Ann. New York Acad. Sci. 319 (1979), 71-81.
Duffus, D. A., Kierstead, H. A. and Snevily, H. S.: An explicit 1-factorization in the middle of the Boolean lattice, J. Combin. Theory, Ser. A 65 (1994), 334-342.
Godsil, C. D.: More odd graph theory, Discrete Math. 32 (1980), 205-207.
Hammond, P. and Smith, D. H.: Perfect codes in the graphs O k, J. Combin. Theory, Ser. B 19 (1975), 239-255.
Kierstead, H. A. and Trotter, W. T.: Explicit matchings in the middle levels of the Boolean lattice, Order 5 (1988), 163-171.
Lovász, L.: Problem 11, In: Combinatorial Structures and their Applications, Gorden and Breach, London, 1970.
Mather, M.: The Rugby footballers of Croam, J. Combin. Theory, Ser. B 20 (1976), 62-63.
Meredith, G. H. and Lloyd, E. K.: The footballers of Croam, J. Combin. Theory, Ser. B 15 (1973), 161-166.
Savage, C. D. and Shields, I.: A note on Hamilton cyles in Kneser graphs, Preprint.
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Johnson, J.R., Kierstead, H.A. Explicit 2-Factorisations of the Odd Graph. Order 21, 19–27 (2004). https://doi.org/10.1007/s11083-004-3344-x
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DOI: https://doi.org/10.1007/s11083-004-3344-x