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Do 3n − 5 edges force a subdivision of K5?

✍ Scribed by André E. Kézdy; Patrick J. McGuinness

Publisher
John Wiley and Sons
Year
1991
Tongue
English
Weight
645 KB
Volume
15
Category
Article
ISSN
0364-9024

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✦ Synopsis

Abstract

A conjecture of Dirac states that every simple graph with n vertices and 3__n__ − 5 edges must contain a subdivision of K~5~. We prove that a topologically minimal counterexample is 5‐connected, and that no minor‐minimal counterexample contains K~4~ – e. Consequently, Dirac's conjecture holds for all graphs that can be embedded in a surface with Euler characteristic at least − 2.

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