Abstract:The aim of this paper is to classify all snarks up to order 36 and explain the reasons of their uncolourability. The crucial part of our approach is a computerassisted structural analysis of cyclically 5-connected critical snarks, which is justified by the fact that every other snark can be constructed from them by a series of simple operations while preserving uncolourability. Our results reveal that most of the analysed snarks are built up from pieces of the Petersen graph and can be naturally distributed in… Show more
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