In this paper, we investigate whether the symbolic and ordinary powers of a binomial edge ideal JG are equal. We show that the equalityG holds for every t ≥ 1 when | Ass(JG)| = 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 JG occurs.
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