Very well-covered graphs via the Rees algebra

DOI10.1007/s00009-024-02678-1zbMATH Open1542.13004MaRDI QIDQ6566713

Antonino Ficarra, Marilena Crupi

Publication date: 3 July 2024

Published in: Mediterranean Journal of Mathematics (Search for Journal in Brave)

zbMATH Keywords

monomial idealsRees algebrasedge idealsnormal ringscover idealsvery well-covered graphs

Mathematics Subject Classification ID

Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.) (13H10) Commutative rings defined by monomial ideals; Stanley-Reisner face rings; simplicial complexes (13F55) Associated graded rings of ideals (Rees ring, form ring), analytic spread and related topics (13A30)

Cites Work

• Persistence and stability properties of powers of ideals
• Powers of the vertex cover ideals
• Vertex decomposability and regularity of very well-covered graphs
• Cohen-Macaulay Rees algebras and their specialization
• Ideals of fiber type and polymatroids
• On the associated graded ring of an ideal
• Arithmetic of normal Rees algebras
• Multigraded shifts of matroidal ideals
• Cohen-Macaulay graphs
• Very well covered graphs
• Powers of componentwise linear ideals: the Herzog-Hibi-Ohsugi conjecture and related problems
• Very well-covered graphs and local cohomology of their residue rings by the edge ideals
• Dominating ideals and closed neighborhood ideals of graphs
• Homological shift ideals
• A glimpse to most of the old and new results on very well-covered graphs from the viewpoint of commutative algebra
• THE PROJECTIVE DIMENSION OF THE EDGE IDEAL OF A VERY WELL-COVERED GRAPH
• Splittings of monomial ideals
• The asymptotic nature of the analytic spread
• Symbolic powers of cover ideal of very well-covered and bipartite graphs
• Monomial Ideals
• LINEAR QUOTIENTS AND MULTIGRADED SHIFTS OF BOREL IDEALS
• Monomial Algebras
• Cohen-Macaulay edge ideal whose height is half of the number of vertices
• Bounds For Invariants of Edge-Rings
• Rings of Invariants of Tori, Cohen-Macaulay Rings Generated by Monomials, and Polytopes
• Restricted classes of veronese type ideals and algebras
• Some homological properties of Borel type ideals
• Dirac's theorem and multigraded syzygies
• Very well-covered graphs by Betti splittings
• Linear resolutions of t-spread lexsegment ideals via Betti splittings
• Normality and associated primes of closed neighborhood ideals and dominating ideals

This page was built for publication: Very well-covered graphs via the Rees algebra