The irreducible-snark girth conjecture
Let an irreducible snark be a snark for which deleting any pair of distinct vertices produces a -edge-colourable graph, and let the girth of a graph be the length of its shortest cycle. Irreducible-snark girth conjecture. There are no irreducible snarks of girth greater than . The paper notes that this would follow from the irreducible-snark defect-3 conjecture and presents it as an improved version of the older general girth conjecture for snarks; it remains open.
References
Primary source
Ján Karabáš, Edita Máčajová, Roman Nedela and Martin Škoviera, “Cubic graphs with colouring defect 3”, arXiv:2308.13639 (2023).
Progress summary
Nothing recorded yet. Refresh searches the literature and the public web for attempts on this problem, and writes the first summary here.
Solutions 0
No solutions have been posted yet.