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K5-Subdivisions in Graphs

Published online by Cambridge University Press:  12 September 2008

Carsten Thomassen
Carsten Thomassen
Affiliation:
Mathematical Institute, Technical University of Denmark, DK-2800 Lyngby, Denmark
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Abstract

In 1964 Dirac conjectured that every graph with n vertices and at least 3n − 5 edges contains a subdivision of K5 We prove a weakened version with 7/2;n − 7 instead of 3n − 5. We prove that, for any prescribed vertex νo, the subdivision can be found such that νo is not one of the five branch vertices. This variant of Dirac's problem, which was suggested by the present author in 1973, is best possible in the sense that 7/2;n − 7 cannot be replaced by 7/2;n − 15/2;.

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Type
Research Article
Information
Combinatorics, Probability and Computing , Volume 5 , Issue 2 , June 1996 , pp. 179 - 189
Copyright
Copyright © Cambridge University Press 1996

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