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On a characterization of planar graphs

Published online by Cambridge University Press:  17 April 2009

C. C. Chen
C. C. Chen
Affiliation:
Department of Mathematics, National University of Singapore, Bukit Timah Road, Singapore 1025, Republic of Singapore.
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Abstract

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By introducing the concept of a polygon-extension of a planar graph, we provide a simple proof that a graph is planar if and only if every strict elegant ring in the graph is even.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 24 , Issue 2 , October 1981 , pp. 289 - 294
Copyright
Copyright © Australian Mathematical Society 1981

References

[1]Kuratowski, Casimir, “Sur le problème des courbes gauches en topolgie”, Fund. Math. 15 (1930), 271–283.CrossRefGoogle Scholar
[2]Little, Charles H.C., “A conjecture about circuits in planar graphs”, Combinatorial Mathematics III, 171–175 (Lecture Notes in Mathematics, 452. Springer-Verlag, Berlin, Heidelberg, New York, 1975).CrossRefGoogle Scholar
[3]Holton, D.A. and Little, C.H.C., “Elegant odd rings and non-planar graphs”,Proceedings of the Eighth Australian Conference in Combinatorial Mathematics (to appear).Google Scholar