Skip to main content Accesibility Help

On the thickness of the complete bipartite graph

  • Lowell W. Beineke (a1), Frank Harary (a1) and John W. Moon (a1)

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.

Hide All
(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), 569579
(2)Errera, A.Un théorème sur les liaisons. C.R. Acad. Sci. Paris, 177 (1923), 489491
(3)Marsh, D. C. B.Solution to problem E 1465. American Math. Monthly, 68 (1961), 1009.
(4)Tutte, W. T.On the non-biplanar character of the complete 9-graph. Canad. Math. Bull. (to appear in 1963).
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
Please enter your name
Please enter a valid email address
Who would you like to send this to? *


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed