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Shortness coefficient of cyclically 4-edge-connected cubic graphs

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Abstract
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.
Keywords
Theoretical Computer Science, Computational Theory and Mathematics, Geometry and Topology, LONGEST CYCLES, CIRCUMFERENCE, PATHS

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MLA
Lo, On-Hei S., et al. “Shortness Coefficient of Cyclically 4-Edge-Connected Cubic Graphs.” ELECTRONIC JOURNAL OF COMBINATORICS, vol. 27, no. 1, 2020, doi:10.37236/8440.
APA
Lo, O.-H. S., Schmidt, J. M., Van Cleemput, N., & Zamfirescu, C. (2020). Shortness coefficient of cyclically 4-edge-connected cubic graphs. ELECTRONIC JOURNAL OF COMBINATORICS, 27(1). https://doi.org/10.37236/8440
Chicago author-date
Lo, On-Hei S., Jens M. Schmidt, Nicolas Van Cleemput, and Carol Zamfirescu. 2020. “Shortness Coefficient of Cyclically 4-Edge-Connected Cubic Graphs.” ELECTRONIC JOURNAL OF COMBINATORICS 27 (1). https://doi.org/10.37236/8440.
Chicago author-date (all authors)
Lo, On-Hei S., Jens M. Schmidt, Nicolas Van Cleemput, and Carol Zamfirescu. 2020. “Shortness Coefficient of Cyclically 4-Edge-Connected Cubic Graphs.” ELECTRONIC JOURNAL OF COMBINATORICS 27 (1). doi:10.37236/8440.
Vancouver
1.
Lo O-HS, Schmidt JM, Van Cleemput N, Zamfirescu C. Shortness coefficient of cyclically 4-edge-connected cubic graphs. ELECTRONIC JOURNAL OF COMBINATORICS. 2020;27(1).
IEEE
[1]
O.-H. S. Lo, J. M. Schmidt, N. Van Cleemput, and C. Zamfirescu, “Shortness coefficient of cyclically 4-edge-connected cubic graphs,” ELECTRONIC JOURNAL OF COMBINATORICS, vol. 27, no. 1, 2020.
@article{8655118,
  abstract     = {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.},
  articleno    = {P1.43},
  author       = {Lo, On-Hei S. and Schmidt, Jens M. and Van Cleemput, Nicolas and Zamfirescu, Carol},
  issn         = {1077-8926},
  journal      = {ELECTRONIC JOURNAL OF COMBINATORICS},
  keywords     = {Theoretical Computer Science,Computational Theory and Mathematics,Geometry and Topology,LONGEST CYCLES,CIRCUMFERENCE,PATHS},
  language     = {eng},
  number       = {1},
  pages        = {14},
  title        = {Shortness coefficient of cyclically 4-edge-connected cubic graphs},
  url          = {http://dx.doi.org/10.37236/8440},
  volume       = {27},
  year         = {2020},
}

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