Table of Contents
International Journal of Combinatorics
Volume 2013, Article ID 725809, 7 pages
http://dx.doi.org/10.1155/2013/725809
Research Article

On Cayley Digraphs That Do Not Have Hamiltonian Paths

Department of Mathematics and Computer Science, University of Lethbridge, Lethbridge, AB, Canada T1K 3M4

Received 23 June 2013; Accepted 4 November 2013

Academic Editor: Jun-Ming Xu

Copyright © 2013 Dave Witte Morris. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. K. Kutnar, D. Marušič, D. W. Morris, J. Morris, and P. Šparl, “Hamiltonian cycles in Cayley graphs whose order has few prime factors,” Ars Mathematica Contemporanea, vol. 5, no. 1, pp. 27–71, 2012. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. M. B. Nathanson, “Partial products in finite groups,” Discrete Mathematics, vol. 15, no. 2, pp. 201–203, 1976. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. D. W. Morris, “2-generated Cayley digraphs on nilpotent groups have Hamiltonian paths,” Contributions to Discrete Mathematics, vol. 7, no. 1, pp. 41–47, 2012. View at Google Scholar · View at MathSciNet
  4. D. Housman, “Enumeration of Hamiltonian paths in Cayley diagrams,” Aequationes Mathematicae, vol. 23, no. 1, pp. 80–97, 1981. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. D. Witte, “Cayley digraphs of prime-power order are Hamiltonian,” Journal of Combinatorial Theory. Series B, vol. 40, no. 1, pp. 107–112, 1986. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. W. Holsztyński and R. F. E. Strube, “Paths and circuits in finite groups,” Discrete Mathematics, vol. 22, no. 3, pp. 263–272, 1978. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. S. J. Curran and D. Witte, “Hamilton paths in Cartesian products of directed cycles,” in Cycles in Graphs (Burnaby, B.C., 1982), B. R. Alspach and C. D. Godsil, Eds., vol. 115 of North-Holland Math. Stud., pp. 35–74, North-Holland, Amsterdam, The Netherlands, 1985. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. R. A. Rankin, “A campanological problem in group theory,” Mathematical Proceedings of the Cambridge Philosophical Society, vol. 44, pp. 17–25, 1948. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. S. C. Locke and D. Witte, “On non-Hamiltonian circulant digraphs of outdegree three,” Journal of Graph Theory, vol. 30, no. 4, pp. 319–331, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet