Binomial Edge Ideals of Complete Multipartite Graphs

In this article, we prove some results about the binomial edge ideal J G of a complete r-partite graph G = K a 1,…, a r : (1) characterization of unmixedness of J G and Cohen–Macaulayness of the residue ring S/J G , (2) F-purity of S/J G , and (3) the equality of the symbolic and the ordinary powers of J G .