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An extremal function for contractions of graphs

Published online by Cambridge University Press:  24 October 2008

Andrew Thomason
Andrew Thomason
Affiliation:
St John's College, Cambridge, England CB2 1TP†
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Abstract

The function c(p) is defined for positive integers p ≥ 4 by

where > denotes contraction. Random graph examples show

In 1968 Mader showed that c(p) ≤ 8(p − 2) [log2 (p − 2)] and more recently Kostochka showed that p√(log p) is the correct order for c(p). We present a simple argument showing c(p) ≤ 2.68p √(log2p)(l + ο(l)).

Information

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 95 , Issue 2 , March 1984 , pp. 261 - 265
Copyright
Copyright © Cambridge Philosophical Society 1984

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References

REFERENCES

[1]Bollobás, B.. Extremal Graph Theory (Academic Press, 1978).Google Scholar
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[3]Kostochka, A. V.. A lower bound for the Hadwiger number of a graph as a function of the average degree of its vertices. Discret. Analyz. Novosibirsk 38 (1982), 37–58.Google Scholar
[4]Mader, W.. Homomorphiesätze für Graphen. Math. Ann. 178 (1968), 154–168.CrossRefGoogle Scholar