Measures of Edge-Uncolorability of Cubic Graphs

M.A. Fiol, G. Mazzuoccolo, E. Steffen, The Electronic Journal of Combinatorics 25 (2018).

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Journal Article | English
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Abstract
There are many hard conjectures in graph theory, like Tutte's 5-flow conjecture, and the 5-cycle double cover conjecture, which would be true in general if they would be true for cubic graphs. Since most of them are trivially true for 3-edge-colorable cubic graphs, cubic graphs which are not 3-edge-colorable, often called snarks, play a key role in this context. Here, we survey parameters measuring how far apart a non 3-edge-colorable graph is from being 3-edge-colorable. We study their interrelation and prove some new results. Besides getting new insight into the structure of snarks, we show that such measures give partial results with respect to these important conjectures. The paper closes with a list of open problems and conjectures.
Publishing Year
Journal Title
The Electronic Journal of Combinatorics
Volume
25
Issue
4
Article Number
P4.54
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Cite this

Fiol MA, Mazzuoccolo G, Steffen E. Measures of Edge-Uncolorability of Cubic Graphs. The Electronic Journal of Combinatorics. 2018;25(4).
Fiol, M. A., Mazzuoccolo, G., & Steffen, E. (2018). Measures of Edge-Uncolorability of Cubic Graphs. The Electronic Journal of Combinatorics, 25(4).
@article{Fiol_Mazzuoccolo_Steffen_2018, title={Measures of Edge-Uncolorability of Cubic Graphs}, volume={25}, number={4P4.54}, journal={The Electronic Journal of Combinatorics}, author={Fiol, M. A. and Mazzuoccolo, Guiseppe and Steffen, Eckhard}, year={2018} }
Fiol, M. A., Guiseppe Mazzuoccolo, and Eckhard Steffen. “Measures of Edge-Uncolorability of Cubic Graphs.” The Electronic Journal of Combinatorics 25, no. 4 (2018).
M. A. Fiol, G. Mazzuoccolo, and E. Steffen, “Measures of Edge-Uncolorability of Cubic Graphs,” The Electronic Journal of Combinatorics, vol. 25, no. 4, 2018.
Fiol, M. A., et al. “Measures of Edge-Uncolorability of Cubic Graphs.” The Electronic Journal of Combinatorics, vol. 25, no. 4, P4.54, 2018.

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