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A survey on snarks and new results: Products, reducibility and a computer search

✍ Scribed by Cavicchioli, A.; Meschiari, M.; Ruini, B.; Spaggiari, F.

Publisher
John Wiley and Sons
Year
1998
Tongue
English
Weight
566 KB
Volume
28
Category
Article
ISSN
0364-9024

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✦ Synopsis

In this paper we survey recent results and problems of both theoretical and algorithmic character on the construction of snarks-non-trivial cubic graphs of class two, of cyclic edge-connectivity at least 4 and with girth β‰₯ 5. We next study the process, also considered by Cameron, Chetwynd, Watkins, Isaacs, Nedela, and Ε koviera, of splitting a snark into smaller snarks which compose it. This motivates an attempt to classify snarks by recognizing irreducible and prime snarks and proving that all snarks can be constructed from them. As a consequence of these splitting operations, it follows that any snark (other than the Petersen graph) of order ≀ 26 can be built as either a dot product or a square product of two smaller snarks. Using a new computer algorithm we have confirmed the computations of Brinkmann and Steffen on the classification of all snarks of order less than 30. Our

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