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Note on T-Minimal Complete Bipartite Graphs

Published online by Cambridge University Press:  20 November 2018

I. Z. Bouwer  and
I. Broere
I. Z. Bouwer
Affiliation:
University of Waterloo
I. Broere
Affiliation:
University of Waterloo
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The thickness of a graph G is the smallest natural number t such that G is the union of t planar subgraphs. A graph G is t-minimal if its thickness is t and if every proper subgraph of G has thickness < t. (These terms were introduced by Tutte in [3]. In [1, p. 51] Beineke employs the term t-critical instead of t-minimal.) The complete bipartite graph K(m, n) consists of m 'dark1 points, n 'light' points, and the mn lines joining points of different types.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 11 , Issue 5 , December 1968 , pp. 729 - 732
Copyright
Copyright © Canadian Mathematical Society 1968

References

1. Beineke, L. W., Complete bipartite graphs: decomposition into planar subgraphs, Lecture 7 in F. Harary, A seminar on graph theory (Holt, Rinehart and Winston, New York, 1967).Google Scholar
2. Beineke, L. W., Harary, F., and Moon, J.W., On the thickness of the complete bipartite graph, Proc. Cambridge Philos. Soc. 60 (1964) 1-5.Google Scholar
3. Tutte, W. T., The thickness of a graph, Nederl. Akad. Wetensch. Proc. Ser. A, 66 = Indag. Math. 25 (1963) 567-577.Google Scholar