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On the thickness of the complete bipartite graph

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

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(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).
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Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
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