Extremal Numbers of Hypergraph Suspensions of Even Cycles

Published in European Journal of Combinatorics Vol. 118, May 2024, 103935, 2024

Recommended citation: Mukherjee, Sayan. "Extremal Numbers of Hypergraph Suspensions of Even Cycles." European Journal of Combinatorics Volume 118, May 2024, 103935. https://doi.org/10.1016/j.ejc.2024.103935

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.

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