For a bridgeless cubic graph $G$, $m_3(G)$ is the ratio of the maximum number of edges of $G$ covered by the union of $3$ perfect matchings to $|E(G)|$. We prove that for any $r\in [4/5, 1)$, there exist infinitely many cubic graphs $G$ such that $m_3(G) = r$. For any $r\in [9/10, 1)$, there exist infinitely many cyclically $4$-connected cubic graphs $G$ with $m_3(G) = r$.

翻译：对于无桥三次图$G$，$m_3(G)$表示$G$中能被三个完美匹配的并覆盖的最大边数与$|E(G)|$的比值。我们证明对于任意$r\in [4/5, 1)$，存在无穷多个三次图$G$满足$m_3(G) = r$。对于任意$r\in [9/10, 1)$，存在无穷多个循环$4$-连通三次图$G$满足$m_3(G) = r$。