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Achromatic numbers of random graphs

Published online by Cambridge University Press:  24 October 2008

Colin McDiarmid
Colin McDiarmid
Affiliation:
Wolfson College, Oxford
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Abstract

The achromatic number ψ(G) of a graph G is the greatest number of colours in a proper colouring of the vertices of G such that for every pair of colours some vertex of the first colour and some vertex of the second colour are adjacent. We prove that almost all graphs Gn with n vertices satisfy n/(k+l) < ψ(Gn) < n/(k–1), where k = k(n) = (log2n)½. We show also that the achromatic number is a ‘global’ invariant.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 92 , Issue 1 , July 1982 , pp. 21 - 28
Copyright
Copyright © Cambridge Philosophical Society 1982

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References

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