Affiliation:
1. University of Kurdistan
Abstract
There are two motivating questions in [M. Mahmoudi, A. Mousivand, M. Crupi, G. Rinaldo, N. Terai and S. Yassemi, arXiv:1006.1087v1] and [M. Mahmoudi, A. Mousivand, M. Crupi, G. Rinaldo, N. Terai and S. Yassemi, J. Pure Appl. Algebra, 215(10) (2011), 2473-2480] about Castelnuovo-Mumford regularity and vertex decomposability of simple graphs. In this paper, we give negative answers to the questions by providing two counterexamples.
Publisher
The International Electronic Journal of Algebra
Subject
Algebra and Number Theory
Reference17 articles.
1. H. N. Aziz, A. Mafi and F. Seyfpour, Bi-sequentially Cohen-Macaulay bipartite graphs, to appear in J. Algebra Appl., (2023).
2. J. Earl, K. N. Vander Meulen and A. Van Tuyl, Independence complexes of well-covered circulant Graphs, Exp. Math., 25(4) (2016), 441-451.
3. D. R. Grayson and M. E. Stillman, Macaulay2, a software system for research in algebraic geometry,
Available at http://www.math.uiuc.edu/Macaulay2/.
4. H. T. Ha and A. Van Tuyl, Monomial ideals, edge ideals of hypergraphs, and their graded Betti numbers, J. Algebraic Combin., 27(2) (2008), 215-245.
5. J. Herzog and T. Hibi, Componentwise linear ideals, Nagoya Math. J., 153 (1999), 141-153.