Table of Contents
ISRN Combinatorics
Volume 2013, Article ID 236298, 8 pages
http://dx.doi.org/10.1155/2013/236298
Research Article

Packings and Coverings of Various Complete Graphs with the 4-Cycle with a Pendant Edge

1Department of Computer Science, Francis Marion University, Florence, SC 29502, USA
2Institute of Mathematics and Physics, Aberystwyth University, Aberystwyth, Ceredigion SY23 3BZ, UK
3Department of Mathematics and Statistics, East Tennessee State University, Johnson City, TN 37614, USA

Received 17 June 2013; Accepted 12 August 2013

Academic Editors: C. da Fonseca, P. E. Jorgensen, A. V. Kelarev, and S. Zhou

Copyright © 2013 Brandon Coker et al. 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. T. Kirkman, “On a problem in combinatorics,” Cambridge and Dublin Mathematics Journal, vol. 2, pp. 191–204, 1847. View at Google Scholar
  2. J. Schönheim, “On maximal systems of K-tuples,” Studia Scientiarum Mathematicarum Hungarica, vol. 1, pp. 363–368, 1966. View at Google Scholar · View at MathSciNet
  3. J. Schönheim and A. Bialostocki, “Packing and covering of the complete graph with 4-cycles,” Canadian Mathematical Bulletin, vol. 18, no. 5, pp. 703–708, 1975. View at Google Scholar · View at MathSciNet
  4. A. E. Brouwer, “Optimal packings of K4's into a Kn,” Journal of Combinatorial Theory A, vol. 26, no. 3, pp. 278–297, 1979. View at Publisher · View at Google Scholar · View at MathSciNet
  5. J. A. Kennedy, “Maximum packings of Kn with hexagons,” The Australasian Journal of Combinatorics, vol. 7, pp. 101–110, 1993. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. J. A. Kennedy, “Maximum packings of Kn with hexagons: corrigendum,” The Australasian Journal of Combinatorics, vol. 10, p. 293, 1994. View at Google Scholar · View at MathSciNet
  7. M. K. Fort Jr. and G. A. Hedlund, “Minimal coverings of pairs by triples,” Pacific Journal of Mathematics, vol. 8, pp. 709–719, 1958. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. J. A. Kennedy, “Minimum coverings of Kn with hexagons,” The Australasian Journal of Combinatorics, vol. 16, pp. 295–303, 1997. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. J.-C. Bermond, C. Huang, A. Rosa, and D. Sotteau, “Decomposition of complete graphs into isomorphic subgraphs with five vertices,” Ars Combinatoria, vol. 10, pp. 211–254, 1980. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. J.-C. Bermond and J. Schönheim, “G-decomposition of Kn, where G has four vertices or less,” Discrete Mathematics, vol. 19, no. 2, pp. 113–120, 1977. View at Publisher · View at Google Scholar · View at MathSciNet
  11. Q.-D. Kang, L.-D. Yuan, and S.-X. Liu, “Graph designs for all graphs with six vertices and eight edges,” Acta Mathematicae Applicatae Sinica, vol. 21, no. 3, pp. 469–484, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. Q. Kang, H. Zhao, and C. Ma, “Graph designs for nine graphs with six vertices and nine edges,” Ars Combinatoria, vol. 88, pp. 379–395, 2008. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. B. Coker, G. Coker, and R. Gardner, “Decompositions of various complete graphs into isomorphic copies of the 4-cycle with a pendant edge,” International Journal of Pure and Applied Mathematics, vol. 74, no. 4, pp. 485–492, 2012. View at Google Scholar
  14. D. E. Bryant, D. G. Hoffman, and C. A. Rodger, “5-cycle systems with holes,” Designs, Codes and Cryptography, vol. 8, no. 1-2, pp. 103–108, 1996, Special issue dedicated to Hanfried Lenz. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. D. E. Bryant, C. A. Rodger, and E. R. Spicer, “Embeddings of m-cycle systems and incomplete m-cycle systems: m14,” Discrete Mathematics, vol. 171, no. 1–3, pp. 55–75, 1997. View at Publisher · View at Google Scholar · View at MathSciNet
  16. E. Mendelsohn and A. Rosa, “Embedding maximal packings of triples,” Congressus Numerantium, vol. 40, pp. 235–247, 1983. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  17. R. Gardner and W. Surber, “Restricted and unrestricted hexagon coverings of the complete bipartite graph”.