Abstract
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 \(t \ge 1\) when \(|{\text {Ass}}(J_{G})|=2\). 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.
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Jahani, I., Bayati, S. & Rahmati, F. On the Equality of Symbolic and Ordinary Powers of Binomial Edge Ideals. Bull Braz Math Soc, New Series 54, 7 (2023). https://doi.org/10.1007/s00574-022-00323-7
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DOI: https://doi.org/10.1007/s00574-022-00323-7