On tight cycles in hypergraphs
نویسندگان
چکیده
A tight k-uniform `-cycle, denoted by TC ` , is a k-uniform hypergraph whose vertex set is v0, · · · , v`−1, and the edges are all the k-tuples {vi, vi+1, · · · , vi+k−1}, with subscripts modulo k. Motivated by a classic result in graph theory that every n-vertex cycle-free graph has at most n− 1 edges, Sós and, independently, Verstraëte asked whether for every integer k, a k-uniform n-vertex hypergraph without any tight k-uniform cycles has at most ( n−1 k−1 ) edges. In this paper, we answer this question in negative.
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