4.3 Article

The computational complexity of Holant problems on 3-regular graphs

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Summary: In this research, a complexity classification for Holant problems was established, revealing new tractable problems on planar graphs that cannot be expressed through holographic reduction to FKT. A recurring theme of holographic reduction to FKT was found for #CSP and spin systems problems. However, the conjectured form of a dichotomy for planar #CSPd is false when d >= 5. The study also unveiled a dichotomy for planar #CSP2, which was proven without relying on a more general planar #CSPd dichotomy for d >= 3.

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