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Yip, Chi Hoi
Finite fields and their applications, January 2022, 2022-01-00, Volume: 77Journal Article
Finding a reasonably good upper bound for the clique number of Paley graphs is an open problem in additive combinatorics. A recent breakthrough by Hanson and Petridis using Stepanov's method gives an improved upper bound on Paley graphs defined on a prime field Fp, where p≡1(mod4). We extend their idea to the finite field Fq, where q=p2s+1 for a prime p≡1(mod4) and a non-negative integer s. We show the clique number of the Paley graph over Fp2s+1 is at most min(ps⌈p2⌉,q2+ps+14+2p32ps−1).
