Shortness coefficient of cyclically 4-edge-connected cubic graphs
- Author
- On-Hei S. Lo, Jens M. Schmidt, Nicolas Van Cleemput (UGent) and Carol Zamfirescu (UGent)
- Organization
- 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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Citation
Please use this url to cite or link to this publication: http://hdl.handle.net/1854/LU-8655118
- 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://doi.org/10.37236/8440}},
volume = {{27}},
year = {{2020}},
}
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