奇偶二项边理想的符号幂与普通幂的比较

Nadia Taghipour, Shamila Bayati, Farhad Rahmati
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摘要

本文研究了图的宇称二项边理想的符号幂和普通幂不相等的情况。结果表明,如果$${\mathcal {I}}_{G}$$是图G的宇称二项边理想,则在下列情况下,对于某t,符号幂$${\mathcal {I}}_{G}^{(t)}$$与普通幂$${\mathcal {I}}_{G}^t$$不相等:(i) G的团数大于3;G有一个网;或者(iii) G有一个PT作为诱导子图。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

Comparison of symbolic and ordinary powers of parity binomial edge ideals

Comparison of symbolic and ordinary powers of parity binomial edge ideals
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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