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29 March 2024
 
  » arxiv » 1512.5944

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Generation of cubic graphs and snarks with large girth
Gunnar Brinkmann ; Jan Goedgebeur ;
Date 18 Dec 2015
AbstractWe describe two new algorithms for the generation of all non-isomorphic cubic graphs with girth at least $kge 5$ which are very efficient for $5le k le 7$ and show how these algorithms can be efficiently 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 6 and 7, respectively.
Using these generators we have also generated all non-isomorphic snarks with girth at least 6 up to 38 vertices and show that there are no snarks with girth at least 7 up to 42 vertices. We present and analyse the new list of snarks with girth 6.
Source arXiv, 1512.5944
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