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

Martin Merker
2019 arXiv   pre-print
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].
arXiv:1905.09101v1 fatcat:25uecptxhjakrjiggb5mhfmddu