# Turan Numbers of Hypergraph Suspensions of Even Cycles

Published in arXiv Preprint, 2021

Recommended citation: Mukherjee, Sayan. "Turan Numbers of Hypergraph Suspensions of Even Cycles." arXiv preprint arXiv:2101.06743 (2021).

For fixed $k\ge 2$, determining the order of magnitude of the number of edges in an $n$-vertex bipartite graph not containing $C_{2k}$, the cycle of length $2k$, is a long-standing open problem. We consider an extension of this problem to triple systems. In particular, we prove that the number of triples in an $n$-vertex triple system which does not contain a $C_6$ in the link of any vertex, has order of magnitude $n^{7/3}$. Additionally, we construct new families of dense $C_6$-free bipartite graphs with $n$ vertices and $n^{4/3}$ edges in order of magnitude.