The regularity of binomial edge ideals of graphs

Abstract

In this paper, we study the Castelnuovo-Mumford regularity and the graded Betti numbers of the binomial edge ideals of some classes of graphs. Our special attention is devoted to a conjecture which asserts that the number of maximal cliques of a graph provides an upper bound for the regularity of its binomial edge ideal.

Keywords

• binomial edge ideal
• castelnuovo-mumford regularity
• free cut edge