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 --相关链接-- 西安交通大学研究生院 西安交通大学教务处
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A tight k-uniform $\ell$-cycle, denoted by $TC_\ell^k$, is a k-uniform hypergraph whose vertex set is $v_0, \cdots, v_{\ell-1}$, and the edges are all the k-tuples $\{v_i, v_{i+1}, \cdots, v_{i+k-1}\}$, with subscripts modulo $\ell$. Motivated by a classic result in graph theory that every n-vertex cycle-free graph has at most n-1 edges, S\'os and, independently, Verstra\"ete asked whether for every integer k, a k-uniform n-vertex hypergraph without any tight k-uniform cycles has at most $\binom{n-1}{k-1}$ edges. In this talk I will present a construction giving negative answer to this question, and discuss some related problems. Joint work with Jie Ma.