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Regularity of powers of cover ideals of bipartite graphs

Nguyen Thu Hang

Thai Nguyen University of Sciences, Tan Thinh Ward, Thai Nguyen City, Thai Nguyen, Vietnam

International Centre of Research and Postgraduate Training in Mathematics, 18B Hoang Quoc Viet Street, Ha Noi, Vietnam

E-mail Address: [email protected]

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and

Truong Thi Hien

Hong Duc University, 565 Quang Trung Street, Dong Ve Ward, Thanh Hoa, Viet Nam

E-mail Address: [email protected]

Corresponding author.

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https://doi.org/10.1142/S0218196723500169Cited by:1 (Source: Crossref)

Abstract

Let $G = (V, E)$ be a bipartite graph over the vertex set $V = {1, \dots, r}$ and let $J = J (G)$ be the cover ideal of $G$ in the polynomial ring $R = K [x_{1}, \dots, x_{r}]$ . It is known that there are integers $b$ and $t_{0}$ such that $reg J^{t} = d (J) t + b$ is a linear function in $t$ for all $t \geq t_{0}$ . In this paper, we give effective bounds for $b$ and $t_{0}$ .

Communicated by J. McCullough

Keywords:

AMSC: 13A15, 13C15, 13D45, 05C90, 05E40, 05E45

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