Watkins snark

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Watkins snark
Watkins snark.svg
The Watkins snark
Named after J. J. Watkins
Vertices 50
Edges 75
Chromatic number 3
Chromatic index 4
Properties Snark

In the mathematical field of graph theory, the Watkins snark is a snark with 50 vertices and 75 edges.[1][2] It was discovered by John J. Watkins in 1989.[3]

As a snark, the Watkins graph is a connected, bridgeless cubic graph with chromatic index equal to 4. The Watkins snark is also non-planar and non-hamiltonian.

Another well known snark on 50 vertices is the Szekeres snark, the fifth known snark, discovered by George Szekeres in 1973.[4]

Gallery[edit]

References[edit]

  1. ^ Weisstein, Eric W., "Watkins Snark", MathWorld.
  2. ^ Watkins, J. J. and Wilson, R. J. "A Survey of Snarks." In Graph Theory, Combinatorics, and Applications (Ed. Y. Alavi, G. Chartrand, O. R. Oellermann, and A. J. Schwenk). New York: Wiley, pp. 1129-1144, 1991
  3. ^ Watkins, J. J. "Snarks." Ann. New York Acad. Sci. 576, 606-622, 1989.
  4. ^ Szekeres, G. (1973). "Polyhedral decompositions of cubic graphs". Bull. Austral. Math. Soc. 8 (03): 367–387. doi:10.1017/S0004972700042660.