Standard graded vertex cover algebras, cycles and leaves

By Jürgen Herzog, Takayuki Hibi, Ngô Viêt Trung, Xinxian Zheng. 2006

78 citations recorded by the source corpus.

The aim of this paper is to characterize simplicial complexes which have standard graded vertex cover algebras. This property has several nice consequences for the squarefree monomial ideals defining these algebras. It turns out that such simplicial complexes are closely related to a range of hypergraphs which generalize bipartite graphs and trees. These relationships allow us to obtain very general results on standard graded vertex cover algebras which cover previous major results on Rees algebras of squarefree monomial ideals.

Subfields: Algebra and Number Theory, Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/4b198e219ea05dcec425e4c97baa5e8c5b0fafc1

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

In Computational Theory and Mathematics

In Geometry and Topology

Citations in the corpus

Cohen-Macaulayness of large powers of Stanley-Reisner ideals (2010, background): “xi1 ···xir with {i1,...,ir}∩F 6= ∅for every facet Fof∆, which correspond to covers of the facets of ∆. Note that the equality between ordinary and symbolic powers of J(∆) were already studied in [9], [10]. Using a well known result in matroid theory we are able to derive from Theorem 3.6 the followi”
The stable set of associated prime ideals of a polymatroidal ideal (2011, background): “The simplicial complex Δ has no special odd cycles in the sense of [16].”
Cohen-Macaulayness of monomial ideals and symbolic powers of Stanley-Reisner ideals (2010, background): “the problem when I(m) ∆ = I m ∆ in terms of ∆. The case dim∆ = 1 has been solved in [12]. We don’t address this problem here because it is of diﬀerent nature than the CohenMacaulayness of I(m) ∆ [5], [6]. For unexplained terminology we refer the readers to the books [2], [17] and [19]. Finally, the ”
Resolutions of square-free monomial ideals via facet ideals: a survey (2006, background): “ of edge ideals via the cycle structure of complement graphs; and Zheng [48] calculated the regularity of the edge ideal of a forest from the number of 1Since ﬁrst submitting this paper, some authors [24, 22, 43] have taken the point of view that the monomial generators of a square-free monomial ide”
Monomial ideals, edge ideals of hypergraphs, and their graded Betti numbers (2006, background): “(A hypergraph point of view is also taken in the recent paper [15].”
Edge ideals: algebraic and combinatorial properties (2010, background): “dge ideals and clutters (e.g., Cohen-Macaulayness, unmixedness, normality, normally torsion-freeness, shellability, vertex decomposability, stability of associated primes) is of current interest, see [22, 24, 25, 32, 39, 40, 41, 45, 51, 61, 62, 89, 116] and the references there. In this paper we wil”