On the powers of vertex cover ideals

DOI10.1016/j.jpaa.2021.106808zbMath1468.13026OpenAlexW3175569696MaRDI QIDQ1979328

Ajay Kumar, Rajiv Kumar

Publication date: 2 September 2021

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jpaa.2021.106808

zbMATH Keywords

regularityvertex decomposablesymbolic powerssequentially Cohen-Macaulaycomponentwise linearvertex cover ideal

Mathematics Subject Classification ID

Syzygies, resolutions, complexes and commutative rings (13D02) Cohen-Macaulay modules (13C14) Combinatorial aspects of commutative algebra (05E40)

Related Items

Powers of componentwise linear ideals: the Herzog-Hibi-Ohsugi conjecture and related problems ⋮ Rooted order on minimal generators of powers of some cover ideals ⋮ Regularity of powers of cover ideals of bipartite graphs ⋮ Toric rings arising from vertex cover ideals ⋮ Componentwise linearity of powers of cover ideals ⋮ Powers of vertex cover ideals of simplicial trees

Uses Software

• BoijSoederberg

Cites Work

• Unnamed Item
• Unnamed Item
• Powers of the vertex cover ideals
• Algebraic properties of edge ideals via combinatorial topology
• Resolutions of Stanley-Reisner rings and Alexander duality
• Componentwise linear ideals and Golod rings
• Powers of ideals associated to \((C_{4},2K_{2})\)-free graphs
• Note on bounds for multiplicities
• Regularity of symbolic powers of cover ideals of graphs
• Powers of Componentwise Linear Ideals
• Betti numbers of graded modules and cohomology of vector bundles
• Powers of the Vertex Cover Ideal of a Chordal Graph
• Vertex decomposable graphs and obstructions to shellability
• Sequentially Cohen-Macaulay edge ideals
• Graded Betti numbers of Cohen-Macaulay modules and the multiplicity conjecture
• Shellable Cactus Graphs
• Componentwise linear ideals
• Symbolic powers of cover ideal of very well-covered and bipartite graphs
• Asymptotic behaviour of Castelnuovo-Mumford regularity
• Monomial Ideals