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Powers of the vertex cover ideals

(2014) COLLECTANEA MATHEMATICA. 65(2). p.169-181
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Abstract
We describe a combinatorial condition on a graph which guarantees that all powers of its vertex cover ideal are componentwise linear. Then motivated by Eagon and Reiner's Theorem we study whether all powers of the vertex cover ideal of a Cohen-Macaulay graph have linear free resolutions. After giving a complete characterization of Cohen-Macaulay cactus graphs (i.e., connected graphs in which each edge belongs to at most one cycle) we show that all powers of their vertex cover ideals have linear resolutions.
Keywords
Cohen-Macaulay graphs, Componentwise linear ideals, Edge ideals, Vertex cover ideals of graphs, MACAULAY, RESOLUTIONS

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MLA
Mohammadi, Fatemeh. “Powers of the Vertex Cover Ideals.” COLLECTANEA MATHEMATICA, vol. 65, no. 2, 2014, pp. 169–81, doi:10.1007/s13348-013-0090-7.
APA
Mohammadi, F. (2014). Powers of the vertex cover ideals. COLLECTANEA MATHEMATICA, 65(2), 169–181. https://doi.org/10.1007/s13348-013-0090-7
Chicago author-date
Mohammadi, Fatemeh. 2014. “Powers of the Vertex Cover Ideals.” COLLECTANEA MATHEMATICA 65 (2): 169–81. https://doi.org/10.1007/s13348-013-0090-7.
Chicago author-date (all authors)
Mohammadi, Fatemeh. 2014. “Powers of the Vertex Cover Ideals.” COLLECTANEA MATHEMATICA 65 (2): 169–181. doi:10.1007/s13348-013-0090-7.
Vancouver
1.
Mohammadi F. Powers of the vertex cover ideals. COLLECTANEA MATHEMATICA. 2014;65(2):169–81.
IEEE
[1]
F. Mohammadi, “Powers of the vertex cover ideals,” COLLECTANEA MATHEMATICA, vol. 65, no. 2, pp. 169–181, 2014.
@article{8667481,
  abstract     = {{We describe a combinatorial condition on a graph which guarantees that all powers of its vertex cover ideal are componentwise linear. Then motivated by Eagon and Reiner's Theorem we study whether all powers of the vertex cover ideal of a Cohen-Macaulay graph have linear free resolutions. After giving a complete characterization of Cohen-Macaulay cactus graphs (i.e., connected graphs in which each edge belongs to at most one cycle) we show that all powers of their vertex cover ideals have linear resolutions.}},
  author       = {{Mohammadi, Fatemeh}},
  issn         = {{0010-0757}},
  journal      = {{COLLECTANEA MATHEMATICA}},
  keywords     = {{Cohen-Macaulay graphs,Componentwise linear ideals,Edge ideals,Vertex cover ideals of graphs,MACAULAY,RESOLUTIONS}},
  language     = {{eng}},
  number       = {{2}},
  pages        = {{169--181}},
  title        = {{Powers of the vertex cover ideals}},
  url          = {{http://dx.doi.org/10.1007/s13348-013-0090-7}},
  volume       = {{65}},
  year         = {{2014}},
}

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