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Acta Mathematica Vietnamica

, Volume 42, Issue 3, pp 445–454 | Cite as

Regularity of Powers of Edge Ideals of Some Graphs

Article

Abstract

Let \(\tilde {C_{n}}\) be the graph by adding an ear to C n and \(I=I(\tilde {C_{n}})\) be its edge ideal. In this paper, we prove that \(\operatorname {reg}(I^{s})=2s+\lfloor \frac {n+1}{3}\rfloor -1\) for all s ≥ 1. Let G be the bicyclic graph C m C n with edge ideal I = I(G); we compute the regularity of I s for all s ≥ 1. In particular, in some cases, we get \(\operatorname {reg}(I^{s})=2s+\lfloor \frac {m}{3}\rfloor +\lfloor \frac {n}{3}\rfloor -1\) for all s ≥ 2.

Keywords

Castelnuovo-Mumford regularity Edge ideals Powers of ideals 

Mathematics Subject Classification (2010)

13D02 05E40 05C38 

Notes

Acknowledgments

The author would like to thank Professor Zhongming Tang for his helpful discussion and S. A. Seyed Fakhari for his valuable suggestions. The author is also grateful to the referee for his/her nice comments.

This work was supported by the National Natural Science Foundation of China (11501397), the Natural Science Foundation of Jiangsu Province (BK20140300), and the Jiangsu Government Scholarship for Overseas Studies.

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Copyright information

© Institute of Mathematics, Vietnam Academy of Science and Technology (VAST) and Springer Science+Business Media Singapore 2017

Authors and Affiliations

  1. 1.School of Mathematical SciencesSoochow UniversitySuzhouChina

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