The v-number and Castelnuovo–Mumford regularity of graphs

Civan, Yusuf

doi:10.1007/s10801-022-01164-9

Search citation statements

Order By: Relevance

Paper Sections

Select...

Introduction2

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2023

2024

Publication Types

Select...

Article6

Relationship

Self Cite0

Independent6

Authors

Journals

Cited by 7 publications

(2 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The concept of v-number was introduced by Cooper et all in [10], and further studied in [1,8,26,32,33,38,39].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Vector-spread monomial ideals and Eliahou–Kervaire type resolutions

Ficarra

2023

Journal of Algebra

View full text Add to dashboard Cite

“…The concept of v-number was introduced by Cooper et all in [10], and further studied in [1,8,26,32,33,38,39].…”

Section: Introductionmentioning

confidence: 99%

“…We denote the set of associated primes of I by Ass(I), and by Max(I) the set of associated primes of I that are maximal with respect to the inclusion. The concept of v-number was introduced in [7], and further studied in [1,3,5,17,20,25,26,29,30,32]. Let I ⊂ S be a graded ideal and let p ∈ Ass(I).…”

Section: Introductionmentioning

confidence: 99%

Vector-spread monomial ideals and Eliahou–Kervaire type resolutions

Ficarra

2023

Journal of Algebra

View full text Add to dashboard Cite

Connected domination in graphs and v-numbers of binomial edge ideals

Jaramillo-Velez,

Seccia

2023

Collect. Math.

View full text Add to dashboard Cite

The v-number of a graded ideal is an algebraic invariant introduced by Cooper et al., and originally motivated by problems in algebraic coding theory. In this paper we study the case of binomial edge ideals and we establish a significant connection between their v-numbers and the concept of connected domination in graphs. More specifically, we prove that the localization of the v-number at one of the minimal primes of the binomial edge ideal $$J_G$$ J G of a graph G coincides with the connected domination number of the defining graph, providing a first algebraic description of the connected domination number. As an immediate corollary, we obtain a sharp combinatorial upper bound for the v-number of binomial edge ideals of graphs. Lastly, building on some known results on edge ideals, we analyse how the v-number of $$J_G$$ J G behaves under Gröbner degeneration when G is a closed graph.

show abstract

Simon conjecture and the $$\text{ v }$$-number of monomial ideals

Ficarra

2024

Collect. Math.

View full text Add to dashboard Cite

The v-number and Castelnuovo–Mumford regularity of graphs

Cited by 7 publications

References 12 publications

Vector-spread monomial ideals and Eliahou–Kervaire type resolutions

Vector-spread monomial ideals and Eliahou–Kervaire type resolutions

Connected domination in graphs and v-numbers of binomial edge ideals

Simon conjecture and the $$\text{ v }$$-number of monomial ideals

Contact Info

Product

Resources

About