Hostname: page-component-cd4964975-ppllx Total loading time: 0 Render date: 2023-03-30T14:01:11.506Z Has data issue: true Feature Flags: { "useRatesEcommerce": false } hasContentIssue true


Published online by Cambridge University Press:  31 March 2021

Faculty of Mathematics and Computer Science, Ovidius University, Bd. Mamaia 124, 900527Constanta, Romania
Department of Mathematics, University of Trento, Via Sommarive, 14 38123 Povo (Trento),
Department of Mathematics, Okayama University, 3-1-1, Tsushima-naka, Kita-ku, Okayama, 700-8530,


We study powers of binomial edge ideals associated with closed and block graphs.

© (2021) The Authors. The publishing rights in this article are licenced to Foundation Nagoya Mathematical Journal under an exclusive license

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)


Naoki Terai was supported by the JSPS Grant-in Aid for Scientific Research (C) 18K03244.


Achilles, R. and Vogel, W., Über vollständige Durchschnitte in lokalen Ringen , Math. Nachr. 89 (1979), 285298.CrossRefGoogle Scholar
Almousa, A., Lin, K. N., and Liske, W., Rees algebras of closed determinantal ideals, preprint, arXiv:2008.10950.Google Scholar
Baskoroputro, H., Ene, V., and Ion, C., Koszul binomial edge ideals of pairs of graphs , J. Algebra 515 (2018), 344359.CrossRefGoogle Scholar
Brodmann, M., The asymptotic nature of the analytic spread , Math. Proc. Camb. Philos. Soc. 86 (1979), 3539.CrossRefGoogle Scholar
Busch, A. H., Dragan, F. F., and Shritharan, R., “New min–max theorems for weakly Chordal and dually Chordal graphs” In Combinatorial Optimization and Applications. Part II, Lecture Notes in Comput. Sci. 6509, Springer, Berlin, Heidelberg, 2010, 207218.Google Scholar
Conca, A., De Negri, E., and Gorla, E., Cartwright-Sturmfels ideals associated to graphs and linear spaces , J. Comb. Algebra 2 (2018), no. 3, 231257.CrossRefGoogle Scholar
Conca, A., Herzog, J., and Valla, G., Sagbi bases with applications to blow–up algebras , J. Reine Angew. Math. 474 (1996), 113138.Google Scholar
Cowsik, R. C. and Nori, M. V., On the fibers of blowing up , J. Indian Math. Soc. (N.S.) 40 (1976), 217222.Google Scholar
Crupi, M., and Rinaldo, G., Binomial edge ideals with quadratic Gröbner bases , Electron. J. Comb. 18 (2011), no. 1, # P211, 113.Google Scholar
Crupi, M. and Rinaldo, G., Closed graphs are proper interval graphs , An. Ştiinţ. Univ. “Ovidius” Constanţa Ser. Mat. 22 (2014), no. 3, 3744.Google Scholar
Eisenbud, D. and Huneke, C., Cohen–Macaulay Rees algebras and their specializations , J. Algebra 81 (1983), 202224.CrossRefGoogle Scholar
Ene, V. and Herzog, J., Gröbner bases in Commutative Algebra , Grad. Stud. Math. 130, Amer. Math. Soc., Providence, 2011.Google Scholar
Ene, V. and Herzog, J., “On the symbolic powers of binomial edge ideals”, in (Stamate, D. and Szemberg, T., Eds.), Combinatorial Structures in Algebra and Geometry, Springer Proceedings in Mathematics & Statistics 331, Springer, Berlin, Heidelberg, 2020, 4350.Google Scholar
Ene, V., Herzog, J., and Hibi, T., Cohen-Macaulay binomial edge ideals , Nagoya Math. J. 204 (2011), 5768.CrossRefGoogle Scholar
Ene, V., Herzog, J., and Hibi, T., Mohammadi, F., Determinantal facet ideals , Mich. Math. J. 62 (2013), 3957.10.1307/mmj/1363958240CrossRefGoogle Scholar
Ene, V. and Zarojanu, A., On the regularity of binomial edge ideals , Math. Nachr. 288 (2015), no. 1, 1924.10.1002/mana.201300186CrossRefGoogle Scholar
Grayson, D. and Stillman, M., Macaulay2, a software system for research in algebraic geometry, 2002, Google Scholar
Guardo, E. and Van Tuyl, A., Powers of complete intersections: Graded Betti numbers and applications , Illinois J. Math. 49 (2005), no. 1, 265279.CrossRefGoogle Scholar
, H. T., Trung, N. V., and Trung, T. N., Depth and regularity of powers of sums of ideals , Math. Z. 282 (2016), 819838.CrossRefGoogle Scholar
Herzog, J. and Hibi, T., The depth of powers of an ideal , J. Algebra 291 (2005), 534550.CrossRefGoogle Scholar
Herzog, J. and Hibi, T., Monomial Ideals, Grad. Texts in Math. 260, Springer, London, 2010.Google Scholar
Herzog, J., Hibi, T., Hreinsdóttir, F., Kahle, T., and Rauh, J., Binomial edge ideals and conditional independence statements , Adv. Appl. Math. 45 (2010), 317333.CrossRefGoogle Scholar
Herzog, J., Hibi, T., and Ohsugi, H., Binomial Ideals, Grad. Texts in Math. 279, Springer, London, 2018.Google Scholar
Herzog, J., Asloob Qureshi, A., Persistence and stability properties of powers of ideals , J. Pure Appl. Algebra 219 (2015), 530542.CrossRefGoogle Scholar
Hochster, M., Rings of invariants of tori, Cohen–Macaulay rings generated by monomials, and polytopes , Ann. Math. 96 (1972), 318337.CrossRefGoogle Scholar
Huneke, C., Powers of ideals generated by weak d-sequences , J. Algebra 68 (1981), 471509.10.1016/0021-8693(81)90276-3CrossRefGoogle Scholar
Huneke, C., On the associated graded ring of an ideal , Illinois. J. Math. 26 (1982), 121137.CrossRefGoogle Scholar
Jayanthan, A. V., Kumar, A., and Sarkar, R., Regularity of powers of quadratic sequences with applications to binomial edge ideals , J. Algebra 564 (2020), 98118.CrossRefGoogle Scholar
Jayanthan, A. V., Kumar, A., and Sarkar, R., Almost complete intersection binomial edge ideals and their Rees algebras , J. Pure Appl. Algebra 225 (2021), no. 6, 106628.CrossRefGoogle Scholar
Jayanthan, A. V., Narayanam, N., and Selvaraja, S., Regularity of powers of bipartite graphs , J. Algebr. Combin. 47 (2018), 1738.CrossRefGoogle Scholar
Kimura, K., Terai, N., and Yassemi, S., The projective dimension of the edge ideal of a very well-covered graph , Nagoya Math. J. 230 (2018), 160179.CrossRefGoogle Scholar
Martinez-Bernal, J., Morey, S., and Villarreal, R. H., Associated primes of powers of edge ideals , Collect. Math. 63 (2012), 361374.CrossRefGoogle Scholar
Ohsugi, H. and Hibi, T., Koszul bipartite graphs , Adv. Appl. Math. 22 (1999), 2528.CrossRefGoogle Scholar
Ohtani, M., Graphs and ideals generated by some 2–minors , Comm. Algebra 39 (2011), 905917.CrossRefGoogle Scholar
Rauf, A. and Rinaldo, G., Construction of Cohen-Macaulay binomial edge ideals , Comm. Algebra 42 (2014), no. 1, 2382252.CrossRefGoogle Scholar
Simis, A., Vasconcelos, W. V., and Villarreal, R. H., On the ideal theory of graphs , J. Algebra 167 (1994), no. 2, 389416.CrossRefGoogle Scholar
Trung, T. N., Stability of depths of powers of edge ideals , J. Algebra 452 (2016), 157187.CrossRefGoogle Scholar
Waldi, R., Vollständige durchschnitte in Cohen-Macaulay Ringen , Arch. Math. (Basel) 31 (1978), 439442.CrossRefGoogle Scholar