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Original Articles

On the sequentially Cohen–Macaulay properties of almost complete multipartite graphs

Pages 2478-2493 | Received 01 Oct 2015, Published online: 07 Oct 2016

References

  • Björner, A., Wachs, M. L. (1996). Shellable nonpure complexes and posets. I. Trans. Amer. Math. Soc. 348:1299–1327.
  • Björner, A., Wachs, M. L. (1997). Shellable nonpure complexes and posets. I. Trans. Amer. Math. Soc. 348:3945–3975.
  • Bruns, W., Herzog, J. (1998). Cohen–Macaulay Rings. revised ed. Cambridge Studies in Advanced Mathematics, Vol. 39. Cambridge: Cambridge University Press.
  • Cameron, K. (1989). Induced matchings. Discrete Appl. Math. 24:97–102.
  • Dochtermann, A., Engström, A. (2009). Algebraic properties of edge ideals via combinatorial topology. Electron. J. Combin. 16(2): #R2.
  • Duval, A. M. (1996). Algebraic shifting and sequentially Cohen–Macaulay simplicial complexes. Electron. J. Combin. 3: #R21.
  • Francisco, C. A., Hà, H. T., Van Tuyl, A. (2009). Splittings of monomial ideals. Proc. Amer. Math. Soc. 137:3271–3282.
  • Hà, H. T., Van Tuyl, A. (2008). Monomial ideals, edge ideals of hypergraphs, and their graded Betti numbers. J. Algebraic Combin. 27:215–245.
  • Hachimori, M., Kashiwabara, K. (2011). Obstructions to shellability, partitionability, and sequential Cohen–Macaulayness. J. Combin. Theory, Ser. A 118:1608–1623.
  • Herzog, J., Hibi, T. (2005). Distributive lattices, bipartitegraphs and Alexander duality. J. Algebraic Combin. 22:289–302.
  • Herzog, J., Hibi, T. (2011). Monomial Ideals. Graduate Texts in Mathematics, Vol. 260. London: Springer-Verlag London Limited.
  • Katzman, M. (2006). Characteristic-independence of Betti numbers of graph ideals. J. Combin. Theory Ser. A 113:435–454.
  • Kummini, M. (2009). Regularity, depth and arithmetic rank of bipartite edge ideals. J. Algebraic Combin. 30:429–445.
  • Khosh-Ahang, F., Moradi, S. (2014). Regularity and projective dimension of edge ideal of C5-free vertex decomposable graphs. Proc. Amer. Math. Soc. 142:1567–1576.
  • Kiani, D., Madani, S. S. (2015). The edge ideals of complete multipartite hypergraphs. Commun. Algebra 43:3020–3032.
  • Kiani, D., Seyyedi, S. M. (2009). Vertex decomposable and shellable complete t-partite graphs, Tarbiat Moallem University, 20th Seminar on Algebra, 2-3 Ordibehesht, 1388 (Apr. 22–23, 2009), pp. 106–107.
  • Mahmoudi, M., Mousivand, A., Crupi, M., Rinaldo, G., Terai, N., Yassemi, S. (2011). Vertex decomposability and regularity of very well-covered graphs. J. Pure Appl. Algebra 215:2473–2480.
  • Matsuoka, N., Murai, S. (2016). Uniformly Cohen–Macaulay simplicial complexes and almost Gorenstein simplicial complexes. J. Algebra 455:14–31.
  • Morales, M., Pour, A. A. Y., Zaare-Nahandi, R. (2012). The regularity of edge ideals of graphs. J. Pure Appl. Algebra 216:2714–2719.
  • Morey, S., Reyes, E., Villarreal, R. H. (2008). Cohen–Macaulay, shellable and unmixed clutters with a perfect matching of König type. J. Pure Appl. Algebra 212:1770–1786.
  • Seyyedi, S. M., Rahmati, F., Saeedi, M. Shellable and Cohen–Macaulay complete t-partite graphs. Preprint, arXiv:1204.2112v2.
  • Van Tuyl, A., Villarreal, R. H. (2008). Shellable graphs and sequentially Cohen–Macaulay bipartite graphs. J. Combin. Theory Ser. A 115:799–814.
  • Van Tuyl, A. (2009). Sequentially Cohen–Macaulay bipartite graphs: vertex decomposabilty and regularity. Arch. Math. 93:451–459.
  • Villarreal, R. H. (1990). Cohen–Macaulay graphs. Manuscripta Math. 66:277–293.
  • Woodroofe, R. (2009). Vertex decomposable graphs and obstructions to shellability. Proc. Amer. Math. Soc. 137:3235–3246.
  • Zheng, X. (2004). Resolution of facet ideals. Commun. Algebra 32:2301–2324.

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