Associated primes of powers of edge ideals
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Publication:1956308
DOI10.1007/s13348-011-0045-9zbMath1360.13027arXiv1103.0992OpenAlexW2964312789MaRDI QIDQ1956308
Susan Morey, José Martínez-Bernal, Rafael H. Villarreal
Publication date: 13 June 2013
Published in: Collectanea Mathematica (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1103.0992
Graphs and abstract algebra (groups, rings, fields, etc.) (05C25) Polynomial rings and ideals; rings of integer-valued polynomials (13F20) 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) Structural characterization of families of graphs (05C75) Associated graded rings of ideals (Rees ring, form ring), analytic spread and related topics (13A30) Other special types of modules and ideals in commutative rings (13C13)
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Uses Software
Cites Work
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- Cohen-Macaulay clutters with combinatorial optimization properties and parallelizations of normal edge ideals
- Colorings of hypergraphs, perfect graphs, and associated primes of powers of monomial ideals
- Asymptotic prime divisors
- Rees algebras and polyhedral cones of ideals of vertex covers of perfect graphs
- A conjecture on critical graphs and connections to the persistence of associated primes
- Matching theory
- On the ideal theory of graphs
- The stable set of associated primes of the ideal of a graph
- Cohen-Macaulay graphs
- Combinatorial optimization. Polyhedra and efficiency (3 volumes)
- Algorithmic graph theory and perfect graphs
- The depth of powers of an ideal
- Embedded associated primes of powers of square-free monomial ideals
- Combinatorics of symbolic Rees algebras of edge ideals of clutters
- Asymptotic Prime Divisors and Analytic Spreads
- Asymptotic Stability of Ass(M/I n M)
- Symbolic Rees algebras, vertex covers and irreducible representations of Rees cones
- On prime divisors of \(I^n\), \(n\) large
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