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The Prism Over the Middle-levels Graph is Hamiltonian

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Abstract

Let B k be the bipartite graph defined by the subsets of {1,…,2k + 1} of size k and k + 1. We prove that the prism over B k is hamiltonian. We also show that B k has a closed spanning 2-trail.

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References

  1. Čada, R., Kaiser, T., Rosenfeld, M. and Ryjáček, Z.: Hamiltonian decompositions of prisms over cubic graphs, Discrete Math. 286 (2004), 45–56.

    Article  MathSciNet  Google Scholar 

  2. Duffus, D. A., Kierstead, H. A. and Snevily, H. S.: An explicit 1-factorization in the middle of the Boolean lattice, J. Comb. Theory, Ser. A 65 (1994), 334–342.

    Article  MATH  MathSciNet  Google Scholar 

  3. Duffus, D. A., Sands, B. and Woodrow, R.: Lexicographic matchings cannot form hamiltonian cycles, Order 5 (1988), 149–161.

    Article  MATH  MathSciNet  Google Scholar 

  4. Ellingham, M. N.: Spanning paths, cycles, trees and walks for graphs on surfaces, Congr. Numerantium 115 (1996), 55–90.

    MATH  MathSciNet  Google Scholar 

  5. Havel, I.: Semipaths in directed cubes, in M. Fiedler (ed.), Graphs and Other Combinatorial Topics, Teubner, Leipzig, 1983, pp. 101–108.

    Google Scholar 

  6. Jackson, B. and Wormald, N. C.: k-walks of graphs, Australas. J. Combin. 2 (1990), 135–146.

    MATH  MathSciNet  Google Scholar 

  7. Kaiser, T., Král', D., Rosenfeld, M., Ryjáček Z. and Voss, H.-J.: Hamilton cycles in prisms over graphs, submitted.

  8. Kierstead, H. A. and Trotter, W. T.: Explicit matchings in the middle levels of the Boolean lattice, Order 5 (1988), 163–171.

    Article  MATH  MathSciNet  Google Scholar 

  9. Paulraja, P.: A characterization of hamiltonian prisms, J. Graph Theory 17 (1993), 161–171.

    Article  MATH  MathSciNet  Google Scholar 

  10. Shields, I. and Savage, C.: A Hamilton path heuristic with applications to the Middle two levels problem, Congr. Numerantium 140 (1999), 161–178.

    MATH  MathSciNet  Google Scholar 

  11. Trotter, T.: private communication, 2004.

  12. Zhang, C.-Q.: Integer Flows and Cycle Covers of Graphs, M. Dekker, New York, 1997.

    Google Scholar 

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Authors and Affiliations

  1. IAS, University of Washington, Tacoma, WA, 98402, USA

    Peter Horák

  2. Department of Mathematics and Institute for Theoretical Computer Science, University of West Bohemia, Univerzitní 8, 306 14, Plzeň, Czech Republic

    Tomáš Kaiser & Zdeněk Ryjáček

  3. Institute of Technology, University of Washington, Tacoma, WA, 98402, USA

    Moshe Rosenfeld

Authors
  1. Peter Horák
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  2. Tomáš Kaiser
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  3. Moshe Rosenfeld
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  4. Zdeněk Ryjáček
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Corresponding author

Correspondence to Moshe Rosenfeld.

Additional information

Supported by project 1M0021620808 and Research Plan MSM 4977751301 of the Czech Ministry of Education.

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Horák, P., Kaiser, T., Rosenfeld, M. et al. The Prism Over the Middle-levels Graph is Hamiltonian. Order 22, 73–81 (2005). https://doi.org/10.1007/s11083-005-9008-7

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  • DOI: https://doi.org/10.1007/s11083-005-9008-7

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