We prove that the three-state toric homogenous Markov chain model has Markov
degree two. In algebraic terminology this means, that a certain class of toric
ideals are generated by quadratic binomials. This was conjectured by Haws,
Martin del Campo, Takemura and Yoshida, who proved that they are generated by
binomials of degree six or less.Comment: Updated language and notation. 13page