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http://dx.doi.org/10.4134/BKMS.b171029

A CLASS OF EDGE IDEALS WITH REGULARITY AT MOST FOUR  

Seyedmirzaei, Seyed Abbas (Science and Research Branch Islamic Azad (IAU))
Yassemi, Siamak (School of Mathematics Statistics and Computer Science College of Science University of Tehran)
Publication Information
Bulletin of the Korean Mathematical Society / v.55, no.6, 2018 , pp. 1749-1754 More about this Journal
Abstract
If a graph G is both claw-free and gap-free, then E. Nevo showed that the Castelnuovo-Mumford regularity of the associated edge ideal I(G) is at most three. Later Dao, Huneke and Schwieg gave a simpler proof of this result. In this paper we introduce a class of edge ideals with Castelnuovo-Munmford regularity at most four.
Keywords
Castelnuovo-Mumford regularity; edge ideal;
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1 S. Beyarslan, H. T. Ha, and T. N. Trung, Regularity of powers of forests and cycles, J. Algebraic Combin. 42 (2015), no. 4, 1077-1095.   DOI
2 S. D. Cutkosky, J. Herzog, and N. V. Trung, Asymptotic behaviour of the Castelnuovo-Mumford regularity, Compositio Math. 118 (1999), no. 3, 243-261.   DOI
3 H. Dao, C. Huneke, and J. Schweig, Bounds on the regularity and projective dimension of ideals associated to graphs, J. Algebraic Combin. 38 (2013), no. 1, 37-55.   DOI
4 R. Froberg, On Stanley-Reisner rings, in Topics in algebra, Part 2 (Warsaw, 1988), 57-70, Banach Center Publ., 26, Part 2, PWN, Warsaw, 1990.
5 I. Gitler and C. E. Valencia, Bounds for invariants of edge-rings, Comm. Algebra 33 (2005), no. 5, 1603-1616.   DOI
6 H. T. Ha and A. Van Tuyl, Monomial ideals, edge ideals of hypergraphs, and their graded Betti numbers, J. Algebraic Combin. 27 (2008), no. 2, 215-245.   DOI
7 M. Kummini, Regularity, depth and arithmetic rank of bipartite edge ideals, J. Algebraic Combin. 30 (2009), no. 4, 429-445.   DOI
8 M. Moghimian, S. A. S. Fakhari, and S. Yassemi, Regularity of powers of edge ideal of whiskered cycles, Comm. Algebra 45 (2017), no. 3, 1246-1259.   DOI
9 E. Nevo, Regularity of edge ideals of $C_4$-free graphs via the topology of the lcm-lattice, J. Combin. Theory Ser. A 118 (2011), no. 2, 491-501.   DOI
10 S. A. Seyed Fakhari, Depth, Stanley depth, and regularity of ideals associated to graphs, Arch. Math. (Basel) 107 (2016), no. 5, 461-471.   DOI
11 S. A. Seyed Fakhari and S. Yassemi, Improved bounds for the regularity of edge ideals of graphs, Collect. Math. 69 (2018), no. 2, 249-262.   DOI
12 R. Woodroofe, Matchings, coverings, and Castelnuovo-Mumford regularity, J. Commut. Algebra 6 (2014), no. 2, 287-304.   DOI