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Combinatorica

, Volume 25, Issue 3, pp 307–326 | Cite as

Counting Sets With Small Sumset, And The Clique Number Of Random Cayley Graphs

  • Ben Green*Email author
Original Paper

Given a set A ℤ/Nℤ we may form a Cayley sum graph G A on vertex set ℤ/Nℤ by joining i to j if and only if i+jA. We investigate the extent to which performing this construction with a random set A simulates the generation of a random graph, proving that the clique number of G A is almost surely O(logN). This shows that Cayley sum graphs can furnish good examples of Ramsey graphs. To prove this result we must study the specific structure of set addition on ℤ/Nℤ. Indeed, we also show that the clique number of a random Cayley sum graph on Γ =(ℤ/2ℤ) n is almost surely not O(log |Γ|).

Mathematics Subject Classification (2000):

11B75 

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Copyright information

© János Bolyai Mathematical Society 2005

Authors and Affiliations

  1. 1.Trinity CollegeCambridge CB2 1TQEngland

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