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Regularity of Edge Ideals and Their Powers

  • Arindam Banerjee
  • Selvi Kara BeyarslanEmail author
  • Hà Huy Tài
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 277)

Abstract

We survey recent studies on the Castelnuovo–Mumford regularity of edge ideals of graphs and their powers. Our focus is on bounds and exact values of \(\text {reg}I(G)\) and the asymptotic linear function \(\text {reg}I(G)^q\), for \(q \ge 1\), in terms of combinatorial data of the given graph G.

Keywords

Monomial ideals Edge ideals Regularity Asymptotic linearity 

Notes

Acknowledgements

The authors would like to thank the organizers of SRAC (Southern Regional Algebra Conference) 2017 for their encouragement, which led us to writing this survey. The last named author is partially supported by the Simons Foundation (grant #279786) and Louisiana Board of Regents (grant #LEQSF(2017-19)-ENH-TR-25).

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Arindam Banerjee
    • 1
  • Selvi Kara Beyarslan
    • 2
    Email author
  • Hà Huy Tài
    • 3
  1. 1.Ramakrishna Mission Vivekananda UniversityBelurIndia
  2. 2.Department of Mathematics and StatisticsUniversity of South AlabamaMobileUSA
  3. 3.Department of MathematicsTulane UniversityNew OrleansUSA

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