Stanley–Reisner ideals of higher independence complexes of chordal graphs.
Saved in:
| Title: | Stanley–Reisner ideals of higher independence complexes of chordal graphs. |
|---|---|
| Authors: | Das, Kanoy Kumar1 (AUTHOR) kanoydas0296@gmail.com, Roy, Amit1 (AUTHOR) amitiisermohali493@gmail.com, Saha, Kamalesh2 (AUTHOR) kamalesh.s@srmap.edu.in |
| Source: | International Journal of Algebra & Computation. Jun2026, Vol. 36 Issue 4, p383-406. 24p. |
| Subjects: | Graph theory, Commutative algebra, Cohen-Macaulay rings |
| Abstract: | For t ≥ 2 , the t-independence complex Ind t (G) of a graph G is the collection of all A ⊆ V (G) such that each connected component of the induced subgraph G [ A ] has at most t − 1 vertices. The topology of Ind t (G) is intimately related to the combinatorial property of G. In this paper, we consider the Stanley–Reisner ideal J t (G) of Ind t (G) and focus on its algebraic properties. We prove that for a chordal graph G and for all t, reg (R / J t (G)) = (t − 1) ν t (G) and pd (R / J t (G)) = bight (J t (G)) , where ν t (G) denotes the induced matching number of the corresponding hypergraph of J t (G) , and reg , pd and bight stand for the regularity, projective dimension and big height, respectively. As a consequence of the above results, we combinatorially characterize when the Stanley–Reisner ideal of the t-independence complex of a chordal graph has a linear resolution as well as when it satisfies the Cohen–Macaulay property. The above formulas and their consequences can be seen as a nice generalization of the classical results corresponding to the edge ideals of chordal graphs. [ABSTRACT FROM AUTHOR] |
| Copyright of International Journal of Algebra & Computation is the property of World Scientific Publishing Company and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
| FullText | Text: Availability: 0 |
|---|---|
| Header | DbId: egs DbLabel: Engineering Source An: 193893249 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
| IllustrationInfo | |
| Items | – Name: Title Label: Title Group: Ti Data: Stanley–Reisner ideals of higher independence complexes of chordal graphs. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Das%2C+Kanoy+Kumar%22">Das, Kanoy Kumar</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> kanoydas0296@gmail.com</i><br /><searchLink fieldCode="AR" term="%22Roy%2C+Amit%22">Roy, Amit</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> amitiisermohali493@gmail.com</i><br /><searchLink fieldCode="AR" term="%22Saha%2C+Kamalesh%22">Saha, Kamalesh</searchLink><relatesTo>2</relatesTo> (AUTHOR)<i> kamalesh.s@srmap.edu.in</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22International+Journal+of+Algebra+%26+Computation%22">International Journal of Algebra & Computation</searchLink>. Jun2026, Vol. 36 Issue 4, p383-406. 24p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Graph+theory%22">Graph theory</searchLink><br /><searchLink fieldCode="DE" term="%22Commutative+algebra%22">Commutative algebra</searchLink><br /><searchLink fieldCode="DE" term="%22Cohen-Macaulay+rings%22">Cohen-Macaulay rings</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: For t ≥ 2 , the t-independence complex Ind t (G) of a graph G is the collection of all A ⊆ V (G) such that each connected component of the induced subgraph G [ A ] has at most t − 1 vertices. The topology of Ind t (G) is intimately related to the combinatorial property of G. In this paper, we consider the Stanley–Reisner ideal J t (G) of Ind t (G) and focus on its algebraic properties. We prove that for a chordal graph G and for all t, reg (R / J t (G)) = (t − 1) ν t (G) and pd (R / J t (G)) = bight (J t (G)) , where ν t (G) denotes the induced matching number of the corresponding hypergraph of J t (G) , and reg , pd and bight stand for the regularity, projective dimension and big height, respectively. As a consequence of the above results, we combinatorially characterize when the Stanley–Reisner ideal of the t-independence complex of a chordal graph has a linear resolution as well as when it satisfies the Cohen–Macaulay property. The above formulas and their consequences can be seen as a nice generalization of the classical results corresponding to the edge ideals of chordal graphs. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of International Journal of Algebra & Computation is the property of World Scientific Publishing Company and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
| PLink | https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=egs&AN=193893249 |
| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1142/S021819672650013X Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 24 StartPage: 383 Subjects: – SubjectFull: Graph theory Type: general – SubjectFull: Commutative algebra Type: general – SubjectFull: Cohen-Macaulay rings Type: general Titles: – TitleFull: Stanley–Reisner ideals of higher independence complexes of chordal graphs. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Das, Kanoy Kumar – PersonEntity: Name: NameFull: Roy, Amit – PersonEntity: Name: NameFull: Saha, Kamalesh IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 06 Text: Jun2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 02181967 Numbering: – Type: volume Value: 36 – Type: issue Value: 4 Titles: – TitleFull: International Journal of Algebra & Computation Type: main |
| ResultId | 1 |
