On the Equality of Symbolic and Ordinary Powers of Binomial Edge Ideals

In this paper, we investigate whether the symbolic and ordinary powers of a binomial edge ideal J(G )are equal. We show that the equality J(G)(t)= J(G)((t)) holds for every t >= 1 when | Ass(J(G))| = 2. Moreover, if G is a caterpillar tree, then one has the same equality. Finally, we characterize the generalized caterpillar graphs which the equality of symbolic and ordinary powers of J(G) occurs.