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Communications in Algebra Volume 47, 2019 - Issue 1
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Original Articles

Algebraic properties of toric rings of graphs

Huy Tài HàDepartment of Mathematics, Tulane University, New Orleans, Louisiana, USA; ORCID Iconhttp://orcid.org/0000-0002-6002-3453View further author information
ORCID Icon,
Selvi Kara BeyarslanDepartment of Mathematics and Statistics, University of South Alabama, Mobile, Alabama, USA; ORCID Iconhttp://orcid.org/0000-0002-1464-2659View further author information
ORCID Icon &
Augustine O’KeefeMathematics Department, Connecticut College, New London, Connecticut, USACorrespondence[email protected]
ORCID Iconhttp://orcid.org/0000-0003-1206-8291View further author information
ORCID Icon
Pages 1-16 | Received 26 Sep 2017, Accepted 17 Jan 2018, Published online: 29 Jan 2019

References

  • Aramova, A., Herzog, J. (1996). Koszul cycles and Eliahou-Kervaire type resolutions. J. Algebra. 181(2):347–370.
  • Bertone, C., Micale, V. (2008). On the dimension of the minimal vertex cover semigroup ring of an unmixed bipartite graph. Le Mat. 63(2):157–163.
  • Biermann, J., O'Keefe, A., Van Tuyl, A. (2017). Bounds on the regularity of toric ideals of graphs. Adv. Appl. Math. 85:84–102.
  • Brodmann, M., Sharp, R. (2012). Local Cohomology: An Algebraic Introduction with Geometric Applications (Cambridge Studies in Advanced Mathematics). Cambridge: Cambridge University Press.
  • Corso, A., Nagel, U. (2008). Monomial and toric ideals associated to Ferrers graphs. Trans. Am. Math. Soc. 361(3):1371–1395.
  • Cox, D., Materov, E. (2008). Tate resolutions for Segre embeddings. Ant. Theory. 2(5):523–550.
  • D’Alì, A. (2015). Toric ideals associated with gap-free graphs. J. Pure Appl. Algebra. 219(9):3862–3872.
  • Cox, D., Little, J. B., Schenck, H. K. (2011). Toric Varieties. Graduate Studies in Mathematics, Vol. 124. Providence, RI: American Mathematical Society, xxiv +841 pp.
  • Diestel, R. (2010). Graph Theory. Graduate Texts in Mathematics, Vol. 173, 4th ed. Heidelberg: Springer, xviii +437 pp.
  • Doering, L. R., Gunston, T. (1996). Algebras arising from bipartite planar graphs. Commun. Algebra. 24(11):3589–3598.
  • Eisenbud, D. (1995). Commutative Algebra: With a View toward Algebraic Geometry. Graduate Texts in Mathematics, Vol. 150. New York: Springer-Verlag, xvi +785 pp.
  • Gitler, I., Valencia, C. E. (2005). Multiplicities of edge subrings. Discrete Math. 302(1–3):107–123.
  • Hibi, T., Higashitani, A., Kimura, K., O’Keefe, A. (2011). Depth of edge rings arising from finite graphs. Proc. Am. Math. Soc. 139(11):3807–3813.
  • Hibi, T., Matsuda, K., Ohsugi, H. (2016). Strongly Koszul edge rings. Acta Math. Vietnam. 41(1):69–76.
  • Hochster, M. (1972). Rings of invariants of tori, Cohen–Macaulay rings generated by monomials, and polytopes. Ann. Math. 96(2):318–337.
  • Ohsugi, H., Hibi, T. (1999). Toric ideals generated by quadratic binomials. J. Algebra. 218(2):509–527.
  • Ohsugi, H., Herzog, J., Hibi, T. (2000). Combinatorial pure subrings. Osaka J. Math. 37:745–757.
  • Stückrad, J., Vogel, W. (1978). On Segre products and applications. J. Algebra. 54(2):374–389.
  • Reyes, E., Tatakis, C., Thoma, A. (2012). Minimal generators of toric ideals of graphs. Adv. Appl. Math. 48(1):64–78.
  • Tatakis, C., Thoma, A. (2011). On the universal Gröbner bases of toric ideals of graphs. J. Combin. Theory Ser. A. 118(5):1540–1548.
  • Villarreal, R. H. (1995). Rees algebras of edge ideals. Commun. Algebra. 23(9):3513–3524.

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