The size of Betti tables of edge ideals arising from bipartite graphs

DOI10.1090/proc/16119zbMath1505.13029arXiv2103.04766OpenAlexW3134030026MaRDI QIDQ5039230

Takayuki Hibi, Nursel Erey

Publication date: 12 October 2022

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

Full work available at URL: https://arxiv.org/abs/2103.04766

zbMATH Keywords

projective dimensionbipartite graphCastelnuovo-Mumford regularityedge idealMatching number

Mathematics Subject Classification ID

Graphs and abstract algebra (groups, rings, fields, etc.) (05C25) Commutative rings defined by monomial ideals; Stanley-Reisner face rings; simplicial complexes (13F55) Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.) (05C70) Syzygies, resolutions, complexes and commutative rings (13D02) Combinatorial aspects of commutative algebra (05E40)

Related Items

Comparing invariants of toric ideals of bipartite graphs

Cites Work

• Bounds on the regularity and projective dimension of ideals associated to graphs
• Matchings, coverings, and Castelnuovo-Mumford regularity
• Progress in commutative algebra 1. Combinatorics and homology
• Regularity and \(h\)-polynomials of edge ideals
• Shellable graphs and sequentially Cohen-Macaulay bipartite graphs
• Regularity, depth and arithmetic rank of bipartite edge ideals
• Sequentially Cohen-Macaulay bipartite graphs: Vertex decomposability and regularity
• Regularity of powers of bipartite graphs
• Simplicial trees are sequentially Cohen-Macaulay
• Projective dimension, graph domination parameters, and independence complex homology
• Induced matching numbers of finite graphs and edge ideals
• Regularity 3 in edge ideals associated to bipartite graphs
• Regularity of edge ideals and their powers
• Characteristic-independence of Betti numbers of graph ideals
• Monomial ideals, edge ideals of hypergraphs, and their graded Betti numbers
• Distributive lattices, bipartite graphs and Alexander duality
• \textsc{MAX MIN} vertex cover and the size of Betti tables
• Nonvanishing of Betti Numbers of Edge Ideals and Complete Bipartite Subgraphs
• Non-vanishingness of Betti Numbers of Edge Ideals
• Resolutions of Facet Ideals
• Sequentially Cohen-Macaulay edge ideals
• Monomial Ideals
• Homological invariants of Cameron–Walker Graphs
• Regularity and ℎ-polynomials of toric ideals of graphs
• The regularity and h-polynomial of Cameron-Walker graphs
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