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A Dual form of Kuratowski's Theorem

Published online by Cambridge University Press:  20 November 2018

Frank Harary  and
William T. Tutte
Frank Harary
Affiliation:
University of Michigan
William T. Tutte
Affiliation:
University of Waterloo
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The celebrated criterion of Kuratowski [2] for the planarity of a graph G involves the determination of whether G contains a subgraph homeomorphic to K5 or K3, 3 shown in Figure 1.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 8 , Issue 1 , February 1965 , pp. 17 - 20
Copyright
Copyright © Canadian Mathematical Society 1965

References

1. Kagno, I.N., The mapping of graphs on surfaces, J. Math. Phys. 16 (1937) 46-75.Google Scholar
2. Kuratowski, K., Sur le problème des courbes gauches en topologie, Fund. Math. 15 (1930) 271-283.Google Scholar
3. Tutte, W. T., Matroids and graphs, Trans. Amer. Math. Soc. 90 (1959) 527-552.Google Scholar
4. Tutte, W. T., On the problem of decomposing a graph into n connected factors, J. London Math. Soc. 36 (1961) 221-230.Google Scholar