Descartes Snarks


The Descartes snarks are a set of (strong) snarks on 210 vertices and 315 edges discovered by William Tutte in 1948 writing under the pseudonym Blanche Descartes (Descartes 1948; Holton and Sheehan 1993, pp. 93-97). The Descartes snark illustrated above will be implemented in a future version of the Wolfram Language as GraphData["DescartesSnark1"].

Descartes snarks are obtained by replacing each vertex of the Petersen graph with a 9-cycle and each edge with a graph related to the Petersen graph. This procedure can be performed in a number of ways, leading to multiple distinct Descartes snarks.

See also


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Descartes, B. "Network Colorings." Math. Gaz. 32, 67-69, 1948.Holton, D. A. and Sheehan, J. The Petersen Graph. Cambridge, England: Cambridge University Press, pp. 82 and 93-97, 1993.West, D. B. Introduction to Graph Theory, 2nd ed. Englewood Cliffs, NJ: Prentice-Hall, p. 305, 2000.

Cite this as:

Weisstein, Eric W. "Descartes Snarks." From MathWorld--A Wolfram Web Resource.

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