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Kuratowski's theorem

✍ Scribed by Carsten Thomassen

Publisher
John Wiley and Sons
Year
1981
Tongue
English
Weight
925 KB
Volume
5
Category
Article
ISSN
0364-9024

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✦ Synopsis

Abstract

We present three short proofs of Kuratowski's theorem on planarity of graphs and discuss applications, extensions, and some related problems.

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Graphs of small average genus are characterized. In particular, a Kuratowskitype theorem is obtained: except for finitely many graphs, a cutedge-free graph has average genus less than or equal to \(t\) if and only if it is a necklace. We provide a complete list of those exceptions. A Kuratowski-type