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Symbolic powers of cover ideals of graphs and Koszul property

Yan Gu

Soochow University, Soochow College & School of Mathematical Sciences, Suzhou 215006, P. R. China

E-mail Address: guyan@suda.edu.cn

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Huy Tài Hà

Tulane University, Department of Mathematics, 6823 St. Charles Ave., New Orleans, LA 70118, USA

E-mail Address: tha@tulane.edu

Corresponding author.

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, and

Joseph W. Skelton

Tulane University, Department of Mathematics, 6823 St. Charles Ave., New Orleans, LA 70118, USA

E-mail Address: jskelton@tulane.edu

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https://doi.org/10.1142/S0218196721500405Cited by:2 (Source: Crossref)

Abstract

We show that attaching a whisker (or a pendant) at the vertices of a cycle cover of a graph results in a new graph with the following property: all symbolic powers of its cover ideal are Koszul or, equivalently, componentwise linear. This extends previous work where the whiskers were added to all vertices or to the vertices of a vertex cover of the graph.

Communicated by J. McCullough

Keywords:

AMSC: 13D02, 13C13, 13H10, 05E40, 05E45

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