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We describe two new algorithms for the generation of all non‐isomorphic cubic graphs with girth at least    k  ≥  5    that are very efficient for    5  ≤  k  ≤  7    and show how these algorithms can be restricted to generate snarks with girth at least  k .  Our implementation of these algorithms is more than 30, respectively 40 times faster than the previously fastest generator for cubic graphs with girth at least six and seven, respectively.  Using these generators we have also generated all nonisomorphic snarks with girth at least six up to 38 vertices and show that there are no snarks with girth at least seven up to 42 vertices. We present and analyze the new list of snarks with girth 6.

Generation of Cubic Graphs and Snarks with Large Girth