We prove that, for every natural number k, every sufficiently large 3-connected cubic planar graph has a cycle whose length is in $[k,2k+9]$. We also show that this bound is close to being optimal by constructing, for every even $k\ge 4$, an infinite family of 3-connected cubic planar graphs that contain no cycle whose length is in $[k,2k+1]$.

中文翻译：

---

3连通立方平面图的循环谱中的间隙

我们证明，对于每个自然数k，每个足够大的3连通立方平面图都有一个循环，其长度为$[ķ，2ķ+9]$。我们还表明，通过构造，对于每个偶数，该界限都接近于最优。$ķ\ge 4$，一个由3个连接的立方平面图组成的无穷系列，其中不包含长度为的循环 $[ķ，2ķ+\mathrm{1个}]$。