Lo, On-Hei SolomonOn-Hei SolomonLoSchmidt, Jens M.Jens M.SchmidtVan Cleemput, NicoNicoVan CleemputZamfirescu, Carol T.Carol T.Zamfirescu2020-10-192020-10-192020-02-07Electronic Journal of Combinatorics: 1 (27): P1.43, 1-14 (2020)http://hdl.handle.net/11420/7601Grünbaum and Malkevitch proved that the shortness coefficient of cyclically 4-edge-connected cubic planar graphs is at most76 77. Recently, this was improved to (Formula Presented) and the question was raised whether this can be strengthened to 42, a natural bound inferred from one of the Faulkner-Younger graphs. We prove that the shortness coefficient of cyclically 4-edge-connected cubic planar graphs is at most 37 38 and that we also get the same value for cyclically 4-edge-connected cubic graphs of genus g for any prescribed genus g ≥ 0. We also show that45 46 is an upper bound for the shortness coefficient of cyclically 4-edge-connected cubic graphs of genus g with face lengths bounded above by some constant larger than 22 for any prescribed g ≥ 0.en1077-892620201112https://creativecommons.org/licenses/by-nd/4.0/MathematikJournal Article10.15480/882.319010.37236/844010.15480/882.3190Journal Article