Binomial Edge Ideals of Complete Multipartite Graphs

Abstract

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 .

Key Words:

• Binomial edge ideals
• Complete multipartite graphs
• F-Purity
• Plücker relations
• Symbolic powers

2010 Mathematics Subject Classification:

• Primary 13F20
• Secondary 05E40

ACKNOWLEDGMENT

The author was partially supported by JSPS Research Fellowships for Young Scientists.

Notes

Communicated by I. Swanson.