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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.
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참고문헌 (11)
참고문헌 신청
S. Beyarslan / 2015 / Regularity of powers of forests and cycles / J. Algebraic Combin 42(4):1077~1095
S. D. Cutkosky / 1999 / Asymptotic behaviour of the Castelnuovo-Mumford regularity / Compositio Math 118(3):243~261
H. Dao / 2013 / Bounds on the regularity and projective dimension of ideals associated to graphs / J. Algebraic Combin 38(1):37~55
I. Gitler / 2005 / Bounds for invariants of edge-rings / Comm. Algebra 33(5):1603~1616
H. T. Ha / 2008 / Monomial ideals, edge ideals of hypergraphs, and their graded Betti numbers / J. Algebraic Combin 27(2):215~245
S. D. Cutkosky / 1999 / Asymptotic behaviour of the Castelnuovo-Mumford regularity / Compositio Math 118(3):243~261
H. Dao / 2013 / Bounds on the regularity and projective dimension of ideals associated to graphs / J. Algebraic Combin 38(1):37~55
I. Gitler / 2005 / Bounds for invariants of edge-rings / Comm. Algebra 33(5):1603~1616
H. T. Ha / 2008 / Monomial ideals, edge ideals of hypergraphs, and their graded Betti numbers / J. Algebraic Combin 27(2):215~245
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