Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-26T04:55:46.408Z Has data issue: false hasContentIssue false
  • English
  • Français

Bounds on the Coarseness of the n-Cube

Published online by Cambridge University Press:  20 November 2018

Jehuda Hartman
Jehuda Hartman*
Affiliation:
Department of Mathematics the University of Alberta Edmonton, Alberta, CanadaT6G 2G1
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The coarseness, c(G), of a graph G is the maximum number of edge disjoint nonplanar subgraphs contained in G For the n-dimensional cube Qn we obtain the inequalities

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 22 , Issue 2 , 01 June 1979 , pp. 171 - 175
Copyright
Copyright © Canadian Mathematical Society 1979

References

1. Beineke, L. W. and Chartrand, G., The coarseness of a graph, Compositio Math. (1966),290-298.Google Scholar
2. Beineke, L. W. and Guy, R. K., The coarseness of the complete bipartite graph, Canad. J. Math. 21 (1969), 1086-1096. Google Scholar
3. Guy, R. K. and Beineke, L. W., The coarseness of the complete graph, Canad. J. Math. (1968),888-894.Google Scholar
4. Guy, R. K., A coarseness conjecture of Erdos, J. Comb. Th. 3 (1967),38-42.Google Scholar
5. Harary, F., Graph Theory (Addison-Wesley, Reading, Mass., 1969).Google Scholar
6. Hartman, J., The homeomorphic embedding of Kn in the m-cube, Discrete Math. 16 (1976),157-160.Google Scholar
7. Hartman, J., On homeomorphic embeddings of Km, n in the cube, (submitted for publication).Google Scholar
8. Hartman, J. and Katchalski, M., On k-cycled refinements of certain graphs, (submitted for publication).Google Scholar
9. Kuratowski, K., Sur le problème des courbes gauches en topologie, Fund. Math. 15 (1930),271-283.Google Scholar