Abstract
We prove tight bounds for the crossing number of the n-dimensional hypercube and cube connected cycles (CCC) graphs.
Both authors were supported by a research grant from Humboldt Foundation, Bonn, Germany
This is a preview of subscription content, log in via an institution.
Preview
Unable to display preview. Download preview PDF.
References
Brebner, G., Relating routing graphs and two dimensional array grids, In:Proceedings VLSI: Algorithms and Architectures, North Holland, 1985.
Eggleton, R. B., Guy, R. P., The crossing number of the n-cube, Notices of the American Mathematical Society, 17, 1970, 757.
Erdös, P., Guy, R.P., Crossing number problems, AmericanMathematical Monthly, 80, 1, 1973, 52–58.
Harary, F., Hayes, J. P., Horng-Jyh Wu, A survey of the theory of hypercube graphs, Computers and Mathematics with Applications, 15, 4, 1988, 277–289.
Heath, M. I. (editor), Hypercube Multicomputers, Proceedings of the 2-nd Conference on Hypercube Multicomputers, SIAM, 1987.
Kleitman, D. J., The crossing number of K 5,n , Journal of Combinatorial Theory, 9, 1971, 315–323.
Leighton, F. T., New lower bound techniques for VLSI, In: Proceedings of the 22-nd Annual Symposium on Foundations of Computer Science, 1981, 1–12.
Leiserson, C. E., Area efficient graph layouts (for VLSI), In: Proceedings of the 21-st Annual IEEE Symposium on Foundations of Computer Science, 1980, 270–281.
Kainen, P. C., A lower bound for crossing numbers of graphs with applications to K n ,K p,q , and Q(d), Journal of Combinatorial Theory (B), 12, 1972, 287–298.
Preparata, F. P., Vuillemin, J. E., The cube-connected cycles: a versatile network for parallel computation, In: Proceedings of the 20-th Annual IEEE Symposium on Foundations of Computer Science, 1979, 140–147.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1992 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Sýkora, O., Vrťo, I. (1992). On the crossing number of the hypercube and the cube connected cycles. In: Schmidt, G., Berghammer, R. (eds) Graph-Theoretic Concepts in Computer Science. WG 1991. Lecture Notes in Computer Science, vol 570. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-55121-2_21
Download citation
DOI: https://doi.org/10.1007/3-540-55121-2_21
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-55121-8
Online ISBN: 978-3-540-46735-9
eBook Packages: Springer Book Archive