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Clique number of random Cayley graph  Gyan Prakash
;  Date: 
1 Nov 2007  Abstract:  Let 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 ij 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  Services:  Forum  Review  PDF  Favorites 


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