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].
@article{arxiv.1905.09101,
title = {Gaps in the cycle spectrum of 3-connected cubic planar graphs},
author = {Martin Merker},
journal= {arXiv preprint arXiv:1905.09101},
year = {2019}
}