Durocher–Gunderson–Li–Skala conjecture on cycles in triangle-free graphs

Let $n\geq 4$. A triangle-free graph is a graph containing no triangle, and $K_{a,b}$ denotes the complete bipartite graph with parts of sizes $a$ and $b$. Durocher–Gunderson–Li–Skala conjecture. For each $n\geq 4$, the balanced complete bipartite graph

$$K_{\lceil n/2\rceil, \lfloor n/2 \rfloor}$$

contains more cycles than any other $n$-vertex triangle-free graph. This conjecture asks for the extremal triangle-free graph maximizing the total number of cycles and arose from questions connected with path-finding algorithms. Its status is not resolved in the supplied source.