An upper bound for the regularity of powers of edge ideals
DOI:
https://doi.org/10.7146/math.scand.a-119227Abstract
For a finite simple graph $G$ we give an upper bound for the regularity of the powers of the edge ideal $I(G)$.
References
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Beyarslan, S., Hà, H. T., and Trung, T. N., Regularity of powers of forests and cycles, J. Algebraic Combin. 42 (2015), no. 4, 1077–1095. https://doi.org/10.1007/s10801-015-0617-y
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Cutkosky, S. D., Herzog, J., and Trung, N. V., Asymptotic behaviour of the Castelnuovo-Mumford regularity, Compositio Math. 118 (1999), no. 3, 243–261. https://doi.org/10.1023/A:1001559912258
Eisenbud, D. and Harris, J., Powers of ideals and fibers of morphisms, Math. Res. Lett. 17 (2010), no. 2, 267–273. https://doi.org/10.4310/MRL.2010.v17.n2.a6
Hansen, P., Degrés et nombre de stabilité d'un graphe, Colloque sur la Théorie des Graphes (Paris, 1974), Cahiers Centre Études Rech. Opér. 17 (1975), no. 2–4, 213–220.
Herzog, J., Hibi, T., and Zheng, X., Dirac's theorem on chordal graphs and Alexander duality, European J. Combin. 25 (2004), no. 7, 949–960. https://doi.org/10.1016/j.ejc.2003.12.008
Jayanthan, A. V. and Selvaraja, S., Upper bounds for the regularity of powers of edge ideals of graphs, eprint arXiv:1805.01412 [math.AC], 2018.
Jayanthan, A. V. and Selvaraja, S., Linear polynomial for the regularity of powers of edge ideals of very well covered graphs, J. Commut. Algebra (to appear), eprint arXiv:1708.06883.
Kodiyalam, V., Asymptotic behaviour of Castelnuovo-Mumford regularity, Proc. Amer. Math. Soc. 128 (2000), no. 2, 407–411. https://doi.org/10.1090/S0002-9939-99-05020-0
Seyed Fakhari, S. A. and Yassemi, S., Improved bounds for the regularity of edge ideals of graphs, Collect. Math. 69 (2018), no. 2, 249–262. https://doi.org/10.1007/s13348-017-0204-8
West, D. B., Introduction to graph theory, second ed., Prentice Hall, Inc., Upper Saddle River, NJ, 2001.
Willis, W., Bounds for the independence number of a graph, Master's thesis, Virginia Commonwealth University, 2011, https://scholarscompass.vcu.edu/etd/2575/. https://doi.org/10.25772/B95B-C733
Beyarslan, S., Hà, H. T., and Trung, T. N., Regularity of powers of forests and cycles, J. Algebraic Combin. 42 (2015), no. 4, 1077–1095. https://doi.org/10.1007/s10801-015-0617-y
Conca, A., Regularity jumps for powers of ideals, in “Commutative algebra”, Lect. Notes Pure Appl. Math., vol. 244, Chapman & Hall/CRC, Boca Raton, FL, 2006, pp. 21–32. https://doi.org/10.1201/9781420028324.ch3
Cutkosky, S. D., Herzog, J., and Trung, N. V., Asymptotic behaviour of the Castelnuovo-Mumford regularity, Compositio Math. 118 (1999), no. 3, 243–261. https://doi.org/10.1023/A:1001559912258
Eisenbud, D. and Harris, J., Powers of ideals and fibers of morphisms, Math. Res. Lett. 17 (2010), no. 2, 267–273. https://doi.org/10.4310/MRL.2010.v17.n2.a6
Hansen, P., Degrés et nombre de stabilité d'un graphe, Colloque sur la Théorie des Graphes (Paris, 1974), Cahiers Centre Études Rech. Opér. 17 (1975), no. 2–4, 213–220.
Herzog, J., Hibi, T., and Zheng, X., Dirac's theorem on chordal graphs and Alexander duality, European J. Combin. 25 (2004), no. 7, 949–960. https://doi.org/10.1016/j.ejc.2003.12.008
Jayanthan, A. V. and Selvaraja, S., Upper bounds for the regularity of powers of edge ideals of graphs, eprint arXiv:1805.01412 [math.AC], 2018.
Jayanthan, A. V. and Selvaraja, S., Linear polynomial for the regularity of powers of edge ideals of very well covered graphs, J. Commut. Algebra (to appear), eprint arXiv:1708.06883.
Kodiyalam, V., Asymptotic behaviour of Castelnuovo-Mumford regularity, Proc. Amer. Math. Soc. 128 (2000), no. 2, 407–411. https://doi.org/10.1090/S0002-9939-99-05020-0
Seyed Fakhari, S. A. and Yassemi, S., Improved bounds for the regularity of edge ideals of graphs, Collect. Math. 69 (2018), no. 2, 249–262. https://doi.org/10.1007/s13348-017-0204-8
West, D. B., Introduction to graph theory, second ed., Prentice Hall, Inc., Upper Saddle River, NJ, 2001.
Willis, W., Bounds for the independence number of a graph, Master's thesis, Virginia Commonwealth University, 2011, https://scholarscompass.vcu.edu/etd/2575/. https://doi.org/10.25772/B95B-C733
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Published
2020-05-06
How to Cite
Herzog, J., & Hibi, T. (2020). An upper bound for the regularity of powers of edge ideals. MATHEMATICA SCANDINAVICA, 126(2), 165–169. https://doi.org/10.7146/math.scand.a-119227
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