Generalisation of the frustrated-triangle extremal conjecture to frustrated cycles

Let $G$ be a graph, let $\overline{G}$ denote its complement, and for $k\geq 3$ let $f_k(G)$ be the number of frustrated $k$-cycles, where a cyclic ordering $v_1v_2\dots v_k$ is frustrated when an odd number of its consecutive cycle edges belongs to $G$. For integers $t\geq 0$, let a $(t+1)$-star on $n$ vertices be the graph consisting of a star with $t+1$ leaves together with the remaining isolated vertices. Frustrated-cycle generalisation conjecture. For every $k\geq 3$, $t\geq 0$, and all sufficiently large $n$, if

$$f_k(G)<f_k\big((t+1)\text{-star on }n\text{ vertices}\big),$$

then either $G$ or $\overline{G}$ can be obtained from a complete bipartite graph by flipping at most $t$ edges or non-edges. This proposes an extension of the paper's structural result for frustrated triangles to frustrated cycles; its resolution is not given in the source.