Szekeres snark

Szekeres snark

The Szekeres snark
Named after George Szekeres
Vertices 50
Edges 75
Radius 6
Diameter 7
Girth 5
Automorphisms 20
Chromatic number 3
Chromatic index 4
Properties Snark
Hypohamiltonian

In the mathematical field of graph theory, the Szekeres snark is a snark with 50 vertices and 75 edges.[1] It was the fifth known snark, discovered by George Szekeres in 1973.[2]

As a snark, the Szekeres graph is a connected, bridgeless cubic graph with chromatic index equal to 4. The Szekeres snark is non-planar and non-hamiltonian but is hypohamiltonian.[3]

Another well known snark on 50 vertices is the Watkins snark discovered by John J. Watkins in 1989.[4]

References

  1. Weisstein, Eric W. "Szekeres Snark". MathWorld.
  2. Szekeres, G. (1973). "Polyhedral decompositions of cubic graphs". Bull. Austral. Math. Soc. 8 (3): 367387. doi:10.1017/S0004972700042660.
  3. Weisstein, Eric W. "Hypohamiltonian Graph". MathWorld.
  4. Watkins, J. J. "Snarks." Ann. New York Acad. Sci. 576, 606-622, 1989.
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