Gaps in the cycle spectrum of 3-connected cubic planar graphs

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≥4 , an infinite family of 3-connected cubic planar graphs that contain no cycle whose length is in [k,2k+1]