Regularity of powers of bipartite graphs

DOI10.1007/s10801-017-0767-1zbMath1381.05033arXiv1609.01402OpenAlexW2963249598MaRDI QIDQ1704090

Peng Zhang

Publication date: 8 March 2018

Published in: Journal of Algebraic Combinatorics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1609.01402

zbMATH Keywords

bipartite graphsCastelnuovo-Mumford regularityedge idealinduced matching numberco-chordal cover number

Mathematics Subject Classification ID

Graphs and abstract algebra (groups, rings, fields, etc.) (05C25) Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.) (05C70)

Related Items (38)

The size of Betti tables of edge ideals arising from bipartite graphs ⋮ Asymptotic behavior of integer programming and the stability of the Castelnuovo-Mumford regularity ⋮ Regularity of powers of edge ideals of product of graphs ⋮ POWERS OF BINOMIAL EDGE IDEALS WITH QUADRATIC GRÖBNER BASES ⋮ Regularity of powers of cover ideals of bipartite graphs ⋮ On the Castelnuovo-Mumford regularity of squarefree powers of edge ideals ⋮ Regularity, Rees algebra, and Betti numbers of certain cover ideals ⋮ Regularity of edge ideals via suspension ⋮ Regularity of powers of (parity) binomial edge ideals ⋮ Componentwise linearity of powers of cover ideals ⋮ Regularity of powers of edge ideals: from local properties to global bounds ⋮ Regularity of powers of quadratic sequences with applications to binomial ideals ⋮ Regularity of symbolic powers of edge ideals of Cameron-Walker graphs ⋮ Symbolic powers of edge ideals of graphs ⋮ Regularity and projective dimension of powers of edge ideal of the disjoint union of some weighted oriented gap-free bipartite graphs ⋮ Powers of ideals associated to \((C_{4},2K_{2})\)-free graphs ⋮ A bound for the regularity of powers of edge ideals ⋮ An upper bound for the regularity of powers of edge ideals ⋮ An upper bound for the regularity of symbolic powers of edge ideals of chordal graphs ⋮ Linear polynomials for the regularity of powers of edge ideals of very well-covered graphs ⋮ Fiber invariants of projective morphisms and regularity of powers of ideals ⋮ Upper bounds for the regularity of powers of edge ideals of graphs ⋮ Depth and regularity of monomial ideals via polarization and combinatorial optimization ⋮ Regularity of powers of cover ideals of unimodular hypergraphs ⋮ Geometric regularity of powers of two-dimensional squarefree monomial ideals ⋮ Projective dimension and regularity of powers of edge ideals of vertex-weighted rooted forests ⋮ Symbolic powers of certain cover ideals of graphs ⋮ Regularity of symbolic powers of cover ideals of graphs ⋮ Regularity of powers of edge ideals of unicyclic graphs ⋮ The powers of unmixed bipartite edge ideals ⋮ Homological invariants of powers of fiber products ⋮ Regularity of symbolic powers of edge ideals of unicyclic graphs ⋮ Bounds for the regularity of product of edge ideals ⋮ Regularity of symbolic powers of edge ideals of chordal graphs ⋮ Certain homological invariants of bipartite kneser graphs ⋮ Upper bounds for the regularity of symbolic powers of certain classes of edge ideals ⋮ Regularity and Gröbner bases of the Rees algebra of edge ideals of bipartite graphs ⋮ REGULARITY OF POWERS OF BIPARTITE GRAPHS

Uses Software

• Macaulay2

Cites Work

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• Depth and regularity of powers of sums of ideals
• Bounds on the regularity and projective dimension of ideals associated to graphs
• Vertex-decomposable graphs, codismantlability, Cohen-Macaulayness, and Castelnuovo-Mumford regularity
• Matchings, coverings, and Castelnuovo-Mumford regularity
• Vertex decomposability and regularity of very well-covered graphs
• Prime graphs, matchings and the Castelnuovo-Mumford regularity
• Regularity of powers of forests and cycles
• Regularity, depth and arithmetic rank of bipartite edge ideals
• Sequentially Cohen-Macaulay bipartite graphs: Vertex decomposability and regularity
• Powers of sums and their homological invariants
• Cohen-Macaulay graphs
• \(C_{4}\)-free edge ideals
• Regularity 3 in edge ideals associated to bipartite graphs
• The regularity of powers of edge ideals
• Characteristic-independence of Betti numbers of graph ideals
• Powers of edge ideals of regularity three bipartite graphs
• Monomial ideals, edge ideals of hypergraphs, and their graded Betti numbers
• Regularity of powers of edge Ideal of whiskered cycles
• New Min-Max Theorems for Weakly Chordal and Dually Chordal Graphs
• Resolutions of Facet Ideals
• Combinatorial Commutative Algebra
• Asymptotic behaviour of Castelnuovo-Mumford regularity
• Regularity and projective dimension of the edge ideal of $C_5$-free vertex decomposable graphs
• More characterizations of triangulated graphs
• Dominating induced matchings of finite graphs and regularity of edge ideals

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