Rocky Mountain Journal of Mathematics

Regularity of powers of edge ideals of unicyclic graphs

Ali Alilooee, Selvi Kara Beyarslan, and S. Selvaraja

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Abstract

Let $G$ be a finite simple graph and $I(G)$ denote the corresponding edge ideal. In this paper, we prove that, if $G$ is a unicyclic graph, then, for all $s \geq 1$, the regularity of $I(G)^s$ is exactly $2s+\DeclareMathOperator{reg} (I(G))-2$. We also give a combinatorial characterization of unicyclic graphs with regularity $\nu (G)+1$ and $\nu (G)+2$, where $\nu (G)$ denotes the induced matching number of $G$.

Article information

Source
Rocky Mountain J. Math., Volume 49, Number 3 (2019), 699-728.

Dates
First available in Project Euclid: 23 July 2019

Permanent link to this document
https://projecteuclid.org/euclid.rmjm/1563847229

Digital Object Identifier
doi:10.1216/RMJ-2019-49-3-699

Mathematical Reviews number (MathSciNet)
MR3983296

Zentralblatt MATH identifier
07088332

Subjects
Primary: 05C25: Graphs and abstract algebra (groups, rings, fields, etc.) [See also 20F65] 05C38: Paths and cycles [See also 90B10] 05E40: Combinatorial aspects of commutative algebra 13D02: Syzygies, resolutions, complexes 13F20: Polynomial rings and ideals; rings of integer-valued polynomials [See also 11C08, 13B25]

Keywords
Regularity edge ideal unicyclic graph asymptotic linearity of regularity monomial ideal

Citation

Alilooee, Ali; Beyarslan, Selvi Kara; Selvaraja, S. Regularity of powers of edge ideals of unicyclic graphs. Rocky Mountain J. Math. 49 (2019), no. 3, 699--728. doi:10.1216/RMJ-2019-49-3-699. https://projecteuclid.org/euclid.rmjm/1563847229


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