The three-state toric homogeneous Markov chain model has Markov degree two We prove that the three-state toric homogeneous Markov chain model has Markov degree two. In algebraic terminology this means, that a certain class of toric ideals is generated by quadratic binomials. This was conjectured by Haws, Martin del Campo, Takemura and Yoshida, who proved that they are generated by degree six binomials. 68/Part 2 May-June 285 - 296 285 - 296 Elsevier