Hostname: page-component-78c5997874-8bhkd Total loading time: 0 Render date: 2024-11-14T22:11:02.272Z Has data issue: false hasContentIssue false
  • English
  • Français

On the thickness of the complete bipartite graph

Published online by Cambridge University Press:  24 October 2008

Lowell W. Beineke ,
Frank Harary  and
John W. Moon
Lowell W. Beineke
Affiliation:
University of Michigan and University College London
Frank Harary
Affiliation:
University of Michigan and University College London
John W. Moon
Affiliation:
University of Michigan and University College London
Get access Rights & Permissions [Opens in a new window]

Extract

A graph consists of a finite set of points and a set of lines joining some pairs of these points. At most one line is permitted to join any two points and no point is joined to itself by a line. A graph G′ is a subgraph of the graph G if the points and lines of G′ are also points and lines of G. The union of several graphs having the same set of points is the graph formed by joining two points in this set if they are joined in at least one of the original graphs. A graph is planar if it can be drawn in the plane (or equivalently, on a sphere) so that no lines intersect. The thickness of a graph G is defined as the smallest integer t such that G is the union of t planar subgraphs.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 60 , Issue 1 , January 1964 , pp. 01 - 05
Copyright
Copyright © Cambridge Philosophical Society 1964

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFEBENCES

(1)Battle, J., Harary, F. and Kodama, Y.Every planar graph with nine points has a non-planar complement. Bull. American Math. Soc. 68 (1962), 569–579CrossRefGoogle Scholar
(2)Errera, A.Un théorème sur les liaisons. C.R. Acad. Sci. Paris, 177 (1923), 489–491Google Scholar
(3)Marsh, D. C. B.Solution to problem E 1465. American Math. Monthly, 68 (1961), 1009.Google Scholar
(4)Tutte, W. T.On the non-biplanar character of the complete 9-graph. Canad. Math. Bull. (to appear in 1963).Google Scholar