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A Characterization of Almost-Planar Graphs

Published online by Cambridge University Press:  12 September 2008

Bradley S. Gubser
Bradley S. Gubser
Affiliation:
Department of Mathematics, Hiram College, Hiram, OH 44234, USA Email: [email protected]
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Abstract

Kuratowski's Theorem, perhaps the most famous result in graph theory, states that K5 and K3,3 are the only non-planar graphs for which both G\e, the deletion of the edge e, and G/e, the contraction of the edge e, are planar for all edges e of G. We characterize the almost-planar graphs, those non-planar graphs for which G\e or G/e is planar for all edges e of G. This paper gives two characterizations of the almost-planar graphs: an explicit description of the structure of almost-planar graphs; and an excluded minor criterion. We also give a best possible bound on the number of edges of an almost-planar graph.

Type
Research Article
Information
Combinatorics, Probability and Computing , Volume 5 , Issue 3 , September 1996 , pp. 227 - 245
Copyright
Copyright © Cambridge University Press 1996

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