6-decomposition of snarks
\textit{R. Nedela} and \textit{M. Škoviera} proved in [J. Graph Theory 22, No. 3, 253--279 (1996; Zbl 0856.05082)] that when \(G\) is a snark with a \(k\)-edge cut, \(k\geq 2\), whose removal leaves two \(3\)-colorable components, then they can be both completed into snarks of order at most \(|G|\) by adding at most \(\kappa(k)\) vertices. The values of \(\kappa(k)\) are known for \(k=2,3,4,5\). The authors find a set of 14 complements that suffice to perform \(6\)-decompositions of snarks with at most 30 vertices. They also show that if this set is not complete to perform \(6\)-decompositions of all snarks, then \(\kappa(k) \geq 20\) and there are strong restrictions on the structure of the missing complements, if there are any.
scientific article; zbMATH DE number 6106899