Geodesic
Shortness coefficient of cyclically 4-edge-connected cubic graphs
On-Hei S. Lo1 ; Jens M. Schmidt1 ; Nico Van Cleemput2 ; Carol T. Zamfirescu2
1TU Ilmenau
2Ghent University
The electronic journal of combinatorics, Tome 27 (2020) no. 1
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Grünbaum and Malkevitch proved that the shortness coefficient of cyclically 4-edge-connected cubic planar graphs is at most 76/77. Recently, this was improved to 359/366 (< 52/53) and the question was raised whether this can be strengthened to 41/42, 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 that 45/46 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.
DOI : 10.37236/8440
Classification : 05C40, 05C38, 05C45, 05C10

On-Hei S. Lo  1   ; Jens M. Schmidt  1   ; Nico Van Cleemput  2   ; Carol T. Zamfirescu  2

1 TU Ilmenau
2 Ghent University 
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     title = {Shortness coefficient of cyclically 4-edge-connected cubic graphs},
     journal = {The electronic journal of combinatorics},
     year = {2020},
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     doi = {10.37236/8440},
     zbl = {1432.05059},
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On-Hei S. Lo; Jens M. Schmidt; Nico Van Cleemput; Carol T. Zamfirescu. Shortness coefficient of cyclically 4-edge-connected cubic graphs. The electronic journal of combinatorics, Tome 27 (2020) no. 1. doi: 10.37236/8440

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