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02 November 2024
 
  » arxiv » 0711.0081

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Clique number of random Cayley graph
Gyan Prakash ;
Date 1 Nov 2007
AbstractLet G be a finite abelian group of order n. For any subset B of G with B=-B, the Cayley graph G_B is a graph on vertex set G in which two elements i and j of G are connected by an edge if and only if the element i-j belongs to the set B. It was shown by Ben Green that when G is a vector space over a finite field Z/pZ, then there is a Cayley graph containing neither a complete subgraph nor an independent set of size more than $clog nloglog n,$ where $c>0$ is an absolute constant. In this article we observe that a modification of his arguments show that for an arbitrary finite abelian group, there is a Cayley graph containing neither a complete subgraph nor an independent set of size more than $c(omega^3(n)log omega(n) +loglog n)$, where $c>0$ is an absolute constant and $omega(n)$ denotes the number of distinct prime divisors of $n$.
Source arXiv, 0711.0081
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