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A construction for clique-free pseudorandom graphs

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arxiv 1905.04677 v3 pith:QRFN2E76 submitted 2019-05-12 math.CO

Anurag Bishnoi , Ferdinand Ihringer , Valentina Pepe This is my paper · ORCID
classification math.CO
keywords graphspseudorandomconstructiondensityedgefreehighlytheta
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abstract

A construction of Alon and Krivelevich gives highly pseudorandom $K_k$-free graphs on $n$ vertices with edge density equal to $\Theta(n^{-1/(k -2)})$. In this short note we improve their result by constructing an infinite family of highly pseudorandom $K_k$-free graphs with a higher edge density of $\Theta(n^{-1/(k - 1)})$.

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  1. A note on pseudorandom Ramsey graphs

    math.CO 2019-09 conditional novelty 7.0 of 10

    For fixed s, optimal K_s-free pseudorandom graphs would imply r(s,t)=t^{s-1+o(1)}, and new constructions improve the cycle Ramsey lower bounds to r(C5,t) > t^{11/8} and r(C7,t) > t^{11/9}.

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