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Article overview
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Generation of cubic graphs and snarks with large girth | Gunnar Brinkmann
; Jan Goedgebeur
; | Date: |
18 Dec 2015 | Abstract: | We 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 | Services: | Forum | Review | PDF | Favorites |
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