Szekeres snark

Szekeres snark with 50 tops and 75 edges

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] It has book thickness 3 and queue number 2.^[4]

Another well known snark on 50 vertices is the Watkins snark discovered by John J. Watkins in 1989.^[5]

Gallery

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  The chromatic number of the Szekeres snark is 3.
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  The chromatic index of the Szekeres snark is 4.
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  Alternative drawing of the Szekeres snark.

References

1. Weisstein, Eric W. "Szekeres Snark". MathWorld.
2. Szekeres, G. (1973). "Polyhedral decompositions of cubic graphs". Bull. Austral. Math. Soc. 8 (3): 367–387. doi:10.1017/S0004972700042660.
3. Weisstein, Eric W. "Hypohamiltonian Graph". MathWorld.
4. Wolz, Jessica; Engineering Linear Layouts with SAT. Master Thesis, University of Tübingen, 2018
5. Watkins, J. J. "Snarks." Ann. New York Acad. Sci. 576, 606-622, 1989.