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On the Chromatic Number of Random Cayley Graphs

Part of: Graph theory Additive number theory; partitions

Published online by Cambridge University Press:  09 September 2016

BEN GREEN
BEN GREEN*
Affiliation:
Mathematical Institute, Andrew Wiles Building, Radcliffe Observatory Quarter, Woodstock Road, Oxford OX2 6GG, UK (e-mail: ben.green@maths.ox.ac.uk)
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Abstract

Let G be an abelian group of cardinality n, where hcf(n, 6) = 1, and let A be a random subset of G. Form a graph ΓA on vertex set G by joining x to y if and only if x + y ∈ A. Then, with high probability as n → ∞, the chromatic number χ(ΓA ) is at most $(1 + o(1))\tfrac{n}{2\log_2 n}$ . This is asymptotically sharp when G = ℤ/nℤ, n prime.

MSC classification

Primary: 05C15: Coloring of graphs and hypergraphs
Secondary: 11P70: Inverse problems of additive number theory, including sumsets

Information

Type
Paper
Information
Combinatorics, Probability and Computing , Volume 26 , Issue 2 , March 2017 , pp. 248 - 266
Copyright
Copyright © Cambridge University Press 2016 

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References

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