Lukoťka–Máčajová–Mazák–Škoviera conjecture on the order of cubic graphs of given oddness

Let $G$ be a $2$-edge-connected cubic graph, and let $\omega(G)$ denote its oddness, the minimum number of odd circuits in a $2$-factor of $G$. Lukoťka–Máčajová–Mazák–Škoviera conjecture. The graph $G$ has at least

$$7.5\cdot \omega(G)-5$$

vertices. This proposes a sharper lower bound than the previously proved bound $5.41\cdot\omega(G)$ for bridgeless cubic graphs other than the Petersen graph; the status of the conjecture is not resolved in the supplied source.