DOI QR코드

DOI QR Code

Pascal Triangle and Properties of Bipartite Steinhaus Graphs

  • Received : 2006.02.28
  • Published : 2008.06.30

Abstract

In this paper, we investigate the number of ones in rows of Pascal's Rectangle. Using these results, we determine the existence of regular bipartite Steinhaus graphs. Also, we give an upper bound for the minimum degree of bipartite Steinhaus graphs.

Keywords

References

  1. B. Bollobas, Graph Theory, Springer-Verlag, New York, 1979.
  2. C. K. Bailey and W. M. Dymacek, Regular Steinhaus graphs, Congr. Numer., 66(1988), 45-47.
  3. W. M. Dymacek, Bipartite Steinhaus graphs, Discrete Mathematics, 59(1986) 9-22. https://doi.org/10.1016/0012-365X(86)90064-6
  4. W. M. Dymacek and T. Whaley Generating strings for bipartite Steinhaus graphs, Discrete Mathematics, 141(1995), no 1-3, 95-107. https://doi.org/10.1016/0012-365X(93)E0211-L
  5. W. M. Dymacek, M. Koerlin and T. Whaley A survey of Steinhaus graphs, Proceedings of the Eihgth Quadrennial Intrnational Conference on Graph Theory, Combinatorics, Algorithm and Applications, 313-323, Vol. 1, 1998.
  6. G. J. Chang, B. DasGupta, W. M. Dymacek, M. Furer, M. Koerlin, Y. Lee and T. Whaley, Characterizations of bipartite Steinhaus graphs, Discrete Mathematics, 199(1999) 11-25. https://doi.org/10.1016/S0012-365X(98)00282-9
  7. H. Harborth, Solution of Steinhaus's problem with plus and minus signs, J. Combinatorial Theory, 12(A)(1972), 253-259. https://doi.org/10.1016/0097-3165(72)90039-8
  8. R. Stanley, Enumerative Combinatorics Volume I, Wadsworth, Inc., 1986.
  9. H. Steinhaus, One Hundred Problems in Elementary Mathematics, Dover, New York, 1979.