Szekeres snark

From Wikipedia, the free encyclopedia
Jump to: navigation, search
Szekeres snark
Szekeres snark alt.svg
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]

Gallery[edit]

References[edit]

  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. ^ Watkins, J. J. "Snarks." Ann. New York Acad. Sci. 576, 606-622, 1989.