Szekeres snark

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]

Szekeres snark
The Szekeres snark
Named afterGeorge Szekeres
Vertices50
Edges75
Radius6
Diameter7
Girth5
Automorphisms20
Chromatic number3
Chromatic index4
Book thickness3
Queue number2
PropertiesSnark
Hypohamiltonian
Table of graphs and parameters

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]

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.


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