Geodesic
On the smallest snarks with oddness 4 and connectivity 2
Jan Goedgebeur1
1Ghent University
The electronic journal of combinatorics, Tome 25 (2018) no. 2
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A snark is a bridgeless cubic graph which is not 3-edge-colourable. The oddness of a bridgeless cubic graph is the minimum number of odd components in any 2-factor of the graph.Lukot'ka, Máčajová, Mazák and Škoviera showed in [Electron. J. Combin. 22 (2015)] that the smallest snark with oddness 4 has 28 vertices and remarked that there are exactly two such graphs of that order. However, this remark is incorrect as — using an exhaustive computer search — we show that there are in fact three snarks with oddness 4 on 28 vertices. In this note we present the missing snark and also determine all snarks with oddness 4 up to 34 vertices.
DOI : 10.37236/7327
Classification : 05C30, 05C85
Mots-clés : cubic graph, snark, chromatic index, oddness, computation, exhaustive search

Jan Goedgebeur  1

1 Ghent University 
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Jan Goedgebeur. On the smallest snarks with oddness 4 and connectivity 2. The electronic journal of combinatorics, Tome 25 (2018) no. 2. doi: 10.37236/7327

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