Understanding PPA-completeness

摘要

We show that computation of the SPERNER problem is PPA-complete on the Möbius band under proper boundary conditions, settling a long term open problem. Further, the same computational complexity results extend to other discrete fixed points on the Möbius band, such as the Brouwer fixed point problem, the DPZP fixed point problem and a simple version of the Tucker problem, as well as the projective plane and the Klein bottle. We expect it opens up a new route for further studies on the related combinatorial structures.