Double-star_snark

Double-star snark

Double-star snark

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In the mathematical field of graph theory, the double-star snark is a snark with 30 vertices and 45 edges.[1]

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In 1975, Rufus Isaacs introduced two infinite families of snarks—the flower snark and the BDS snark, a family that includes the two Blanuša snarks, the Descartes snark and the Szekeres snark (BDS stands for Blanuša Descartes Szekeres).[2] Isaacs also discovered one 30-vertex snark that does not belong to the BDS family and that is not a flower snark — the double-star snark.

As a snark, the double-star graph is a connected, bridgeless cubic graph with chromatic index equal to 4. The double-star snark is non-planar and non-hamiltonian but is hypohamiltonian.[3] It has book thickness 3 and queue number 2.[4]

References

  1. [1]
    Weisstein, Eric W. "Double Star Snark". MathWorld.
  2. [2]
    Isaacs, R. (1975), "Infinite families of non-trivial trivalent graphs which are not Tait-colorable", American Mathematical Monthly, 82 (3), Mathematical Association of America: 221–239, doi:10.2307/2319844, JSTOR 2319844
  3. [3]
    Weisstein, Eric W. "Hypohamiltonian Graph". MathWorld.
  4. [4]
    Wolz, Jessica; Engineering Linear Layouts with SAT. Master Thesis, University of Tübingen, 2018


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