The irreducible-snark girth conjecture

Let an irreducible snark be a snark for which deleting any pair of distinct vertices produces a $3$-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 $6$. 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.