Bounding the projective dimension of a squarefree monomial ideal via domination in clutters

DOI10.1090/S0002-9939-2014-12374-4zbMath1306.05036arXiv1301.2665OpenAlexW2100800722MaRDI QIDQ5496298

Hailong Dao, Jay Schweig

Publication date: 30 January 2015

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1301.2665

zbMATH Keywords

edgewise dominationfamily of clutters

Mathematics Subject Classification ID

Hypergraphs (05C65) Planar graphs; geometric and topological aspects of graph theory (05C10) Syzygies, resolutions, complexes and commutative rings (13D02) Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.) (05C69) Combinatorial aspects of simplicial complexes (05E45)

Related Items (12)

ON THE DEPTH OF SYMBOLIC POWERS OF EDGE IDEALS OF GRAPHS ⋮ Initially regular sequences and depths of ideals ⋮ Polarization and depolarization of monomial ideals with application to multi-state system reliability ⋮ Lower bounds for the depth of symbolic powers of edge ideals of graphs ⋮ Bounds on the Stanley depth and Stanley regularity of edge ideals of clutters ⋮ Depth of Powers of Squarefree Monomial Ideals (Research) ⋮ Domination numbers and noncover complexes of hypergraphs ⋮ Regularity and projective dimension of edge ideals ⋮ Projective Dimension of String and Cycle Hypergraphs ⋮ Further applications of clutter domination parameters to projective dimension ⋮ Upper bounds for the regularity of gap-free graphs in terms of minimal triangulation ⋮ Breaking up simplicial homology and subadditivity of syzygies

Cites Work

• Bounds on the regularity and projective dimension of ideals associated to graphs
• Path ideals of rooted trees and their graded Betti numbers
• Chordal and sequentially Cohen-Macaulay clutters
• On rigid circuit graphs
• Extremal problems for transversals in graphs with bounded degree
• Algebraic properties of edge ideals via combinatorial topology
• \(M\)-sequences, graph ideals, and ladder ideals of linear type
• A tree version of Kőnig's theorem
• Projective dimension, graph domination parameters, and independence complex homology
• Local cohomology and pure morphisms
• Depths and Cohen-Macaulay properties of path ideals
• Monomial ideals, edge ideals of hypergraphs, and their graded Betti numbers
• Algebraic Properties of the Path Ideal of a Tree
• Über lokale Kohomologiegruppen hoher Ordnung.
• Graded Betti numbers of path ideals of cycles and lines
• HYPERGRAPHS AND REGULARITY OF SQUARE-FREE MONOMIAL IDEALS

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