Fiol, M. A.
M. A.
Fiol
Mazzuoccolo, Guiseppe
Guiseppe
Mazzuoccolo
Steffen, Eckhard
Eckhard
Steffen
Measures of Edge-Uncolorability of Cubic Graphs
2018
2019-06-05T09:59:10Z
2019-06-07T08:32:57Z
journal_article
https://ris.uni-paderborn.de/record/10129
https://ris.uni-paderborn.de/record/10129.json
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.