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The Coarseness of the Complete Graph

Published online by Cambridge University Press:  20 November 2018

Richard K. Guy  and
Lowell W. Beineke
Richard K. Guy
Affiliation:
University of Calgary, Alberta, Canada; Purdue University
Lowell W. Beineke
Affiliation:
Fort Wayne, Indiana; University College, London, England
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The coarseness, c(G), of a graph G is the maximum number of edge-disjoint, non-planar subgraphs of G. We consider only the complete graph, Kp, on p vertices here. For p = 3r, Erdös conjectured that the coarseness was , but it has been shown (1) that

1

where square brackets denote integer part.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 20 , 1968 , pp. 888 - 894
Copyright
Copyright © Canadian Mathematical Society 1968

Footnotes

To P. Erdös on duplicating the cube for the last time, 26:3:67

References

1. Guy, Richard K., A coarseness conjecture of Erdôs, J. Combinatorial Theory 3 (1967), 38–42.Google Scholar
2. Kuratowski, Kasimir, Sur le problème des courbes gauches en topologie, Fund. Math. 15 1930), 271–283.Google Scholar
3. Rosa, A., On certain valuations of the vertices of a graph, Théorie des graphes, journées internationales d'étude, Rome, 1966 (Dunod, Paris, 1967), 349–355.Google Scholar