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Comparison of symbolic and ordinary powers of parity binomial edge ideals

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Abstract

In this paper, we investigate when symbolic and ordinary powers of the parity binomial edge ideal of a graph fail to be equal. It turns out that if \({\mathcal {I}}_{G}\) is the parity binomial edge ideal of a graph G, then in each of the following cases the symbolic power \({\mathcal {I}}_{G}^{(t)}\) and the ordinary power \({\mathcal {I}}_{G}^t\) are not equal for some t: (i) the clique number of G is greater than 3; (ii) G has a net; or (iii) G has a PT as an induced subgraph.

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic), Tehran, Iran

    Nadia Taghipour, Shamila Bayati & Farhad Rahmati

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  1. Nadia Taghipour
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  2. Shamila Bayati
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  3. Farhad Rahmati
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Correspondence to Shamila Bayati.

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Communicated by Ilse Fischer.

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Taghipour, N., Bayati, S. & Rahmati, F. Comparison of symbolic and ordinary powers of parity binomial edge ideals. Monatsh Math 203, 695–710 (2024). https://doi.org/10.1007/s00605-023-01912-4

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