The Markov basis of $K_{3,N}$
  This document explains how to obtain a Markov basis of the graphical model of the complete bipartite graph $K_{3,N}$ with binary nodes. The computations illustrate the theory developed in arXiv:1404.6392 that explains how to compute Markov bases of toric fiber products. 
Johannes Rauh and Seth Sullivant
math.AC math.ST stat.TH