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Creators/Authors contains: "Liu, Xizhi"

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  1. ; (, The Electronic Journal of Combinatorics)
    An $(n,r,s)$-system is an $$r$$-uniform hypergraph on $$n$$ vertices such that every pair of edges has an intersection of size less than $$s$$. Using probabilistic arguments, Rödl and Šiňajová showed that for all fixed integers $$r> s \ge 2$$, there exists an $(n,r,s)$-system with independence number $$O\left(n^{1-\delta+o(1)}\right)$$ for some optimal constant $$\delta >0$$ only related to $$r$$ and $$s$$. We show that for certain pairs $(r,s)$ with $$s\le r/2$$ there exists an explicit construction of an $(n,r,s)$-system with independence number $$O\left(n^{1-\epsilon}\right)$$, where $$\epsilon > 0$$ is an absolute constant only related to $$r$$ and $$s$$. Previously this was known only for $s>r/2$ by results of Chattopadhyay and Goodman. 
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  2. ; (, Journal of Combinatorial Theory, Series B)
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