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Item type:Publication, Access status: with files , Shortness coefficient of cyclically 4-edge-connected cubic graphs(2020-02-07); ; ; Grünbaum 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.Publicationtype: Journal ArticleScopus© Citations 1 154 115