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Regularity of Edge Ideals and Their Powers

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Advances in Algebra (SRAC 2017)

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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.

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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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Correspondence to Selvi Kara Beyarslan .

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Banerjee, A., Beyarslan, S.K., Huy Tài, H. (2019). Regularity of Edge Ideals and Their Powers. In: Feldvoss, J., Grimley, L., Lewis, D., Pavelescu, A., Pillen, C. (eds) Advances in Algebra. SRAC 2017. Springer Proceedings in Mathematics & Statistics, vol 277. Springer, Cham. https://doi.org/10.1007/978-3-030-11521-0_2

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