Homological invariants of Cameron–Walker Graphs

DOI10.1090/tran/8416zbMath1471.13020arXiv2007.14176OpenAlexW3134311240MaRDI QIDQ5009316

Adam Van Tuyl, Hiroju Kanno, Kyouko Kimura, Takayuki Hibi, Kazunori Matsuda

Publication date: 20 August 2021

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

Full work available at URL: https://arxiv.org/abs/2007.14176

zbMATH Keywords

dimensiondepthCastelnuovo-Mumford regularityedge ideal

Mathematics Subject Classification ID

Commutative rings defined by monomial ideals; Stanley-Reisner face rings; simplicial complexes (13F55) Dimension theory, depth, related commutative rings (catenary, etc.) (13C15) Combinatorial aspects of commutative algebra (05E40) General commutative ring theory and combinatorics (zero-divisor graphs, annihilating-ideal graphs, etc.) (13A70)

Related Items (6)

The size of Betti tables of edge ideals arising from bipartite graphs ⋮ The regularity and h-polynomial of Cameron-Walker graphs ⋮ Behaviors of pairs of dimensions and depths of edge ideals ⋮ Comparing invariants of toric ideals of bipartite graphs ⋮ Matchings and squarefree powers of edge ideals ⋮ Inequalities of invariants on Stanley-Reisner rings of Cohen-Macaulay simplicial complexes

Uses Software

• Macaulay2

Cites Work

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• Algebraic study on Cameron-Walker graphs
• Graded syzygies
• Regularity and \(h\)-polynomials of edge ideals
• Improved bounds for the regularity of edge ideals of graphs
• Projective dimension, graph domination parameters, and independence complex homology
• Induced matching numbers of finite graphs and edge ideals
• Regularity and \(a\)-invariant of Cameron-Walker graphs
• Regularity, matchings and Cameron-Walker graphs
• Characteristic-independence of Betti numbers of graph ideals
• Monomial ideals, edge ideals of hypergraphs, and their graded Betti numbers
• The graphs with maximum induced matching and maximum matching the same size
• Some algebraic invariants of edge ideal of circulant graphs
• Certain algebraic invariants of edge ideals of join of graphs
• Computational methods of commutative algebra and algebraic geometry. With chapters by David Eisenbud, Daniel R. Grayson, Jürgen Herzog and Michael Stillman

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