A characterization of triangle-free Gorenstein graphs and Cohen-Macaulayness of second powers of edge ideals

DOI10.1007/s10801-015-0631-0zbMath1331.05240arXiv1508.07713OpenAlexW2138787867MaRDI QIDQ256536

Do Trong Hoang, Tran Nam Trung

Publication date: 9 March 2016

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

Full work available at URL: https://arxiv.org/abs/1508.07713

zbMATH Keywords

triangle-freeCohen-Macaulayedge idealwell-covered

Mathematics Subject Classification ID

Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Cohen-Macaulay modules (13C14) Combinatorial aspects of simplicial complexes (05E45) Combinatorial aspects of commutative algebra (05E40)

Related Items (16)

Deriving some properties of Stanley-Reisner rings from their squarefree zero-divisor graphs ⋮ Buchsbaumness of the second powers of edge ideals ⋮ Combinatorial characterizations of the Cohen-Macaulayness of the second power of edge ideals ⋮ A classification of 1-well-covered graphs ⋮ On Gorenstein circulant graphs ⋮ \(W_2\)-graphs and shedding vertices ⋮ Line graphs with a Cohen-Macaulay or Gorenstein clique complex ⋮ Gorenstein and Cohen–Macaulay matching complexes ⋮ Trung's construction and the Charney-Davis conjecture ⋮ Cohen-Macaulayness of saturation of the second power of edge ideals ⋮ On Gorenstein graphs ⋮ Improved bounds for the regularity of edge ideals of graphs ⋮ Depth and regularity of monomial ideals via polarization and combinatorial optimization ⋮ The \(v\)-number of edge ideals ⋮ Cohen-Macaulayness of two classes of circulant graphs ⋮ 1-well-covered graphs revisited

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