A characterization of triangle-free Gorenstein graphs and Cohen–Macaulayness of second powers of edge ideals
- 161 Downloads
We graph-theoretically characterize triangle-free Gorenstein graphs G. As an application, we classify when \(I(G)^2\) is Cohen–Macaulay.
KeywordsGraph Triangle-free Well-covered Edge ideal Cohen–Macaulay Gorenstein
Mathematics Subject Classification13D45 05C90 05E40 05E45
We would like to thank Professors L. T. Hoa and N. V. Trung for helpful comments. Part of this work was done while we were at the Vietnam Institute of Advanced Studies in Mathematics (VIASM) in Hanoi, Vietnam. We would like to thank VIASM for its hospitality. We would also like to thank the anonymous referees for many helpful comments.
- 9.Hoang, D.T., Minh, N.C., Trung, T.N.: Cohen Macaulay graphs with large girth. J. Algebra Appl. 14, 1550112 (2015). doi: 10.1142/S0219498815501121
- 11.Miller, E., Sturmfels, B.: Combinatorial commutative algebra. Springer, Berlin (2005)Google Scholar
- 19.Staples, J.: On some subclasses of well-covered graphs, Vanderbilt Univ. Dept. of Math. Ph.D. thesis, (1975)Google Scholar
- 22.Vander Meulen, K.N., Van Tuyl, A., Watt, C.: Cohen–Macaulay circulant graphs. To appear in Comm. Alg. arXiv:1210.8351
- 25.Villarreal, R.: Monomial Algebras, Monographs and Textbooks in Pure and Applied Mathematics, vol. 238. Marcel Dekker, New York (2001)Google Scholar