Regularity and h-polynomials of edge ideals

2018/10/16 by Hibi, Takayuki, Matsuda, Kazunori, Van Tuyl, Adam · 2 citations
#05C69 #05C70 #05E40 #13D02 #13D40 #Combinatorics (math.CO) #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.1810.07140

Abstract

For any two integers d,r ≥ 1, we show that there exists an edge ideal I(G) such that the \rm reg(R/I(G)), the Castelnuovo-Mumford regularity of R/I(G), is r, and \rm deg (h_R/I(G)(t)), the degree of the h-polynomial of R/I(G), is d. Additionally, if G is a graph on n vertices, we show that \rm reg(R/I(G)) + \rm deg (h_R/I(G)(t)) ≤ n.

Cited by

• Hilbert Coefficients and Regularity of Binomial Edge Ideals
• Comparing the v-number and h-polynomials of edge ideals

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