The regularity of powers of edge ideals

By Arindam Banerjee. 2014

115 citations recorded by the source corpus.

In this paper, we prove the existence of a special order on the set of minimal monomial generators of powers of edge ideals of arbitrary graphs. Using this order, we find new upper bounds on the regularity of powers of edge ideals of graphs whose complement does not have any induced four cycles.

Subfields: Algebra and Number Theory, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/ba695da23bbe86bc20e004171ce6f86a28b7f857

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In Algebra and Number Theory

In Computational Theory and Mathematics

Citations in the corpus

Regularity of powers of forests and cycles (2014, methodology): “We recall the following definition and theorem from [3].”
Powers of edge ideals of regularity three bipartite graphs (2014, methodology): “for i 6= j, ei = ej is a possibility) in the spirit of [1].”
Regularity of Edge Ideals and Their Powers (2017, background): “its generators when mis a minimal monomial generator of I(G)s:The even-connection denition is key to attain this goal. We recall the denition of even-connectedness and its important properties from [5]. Denition 3.12. Let G= (V;E) be a graph. Two vertices uand v(umay be the same as v) are said to be”
Symbolic powers of cover ideal of very well-covered and bipartite graphs (2016, unknown): “Computing and finding bounds for the regularity of powers of a monomial ideal have been studied by a number of researchers (see for example [2], [3], [5], [14]).”
Regularity of powers of bipartite graphs (2016, unknown): “Banerjee, in [3], introduced the notion of even-connection with respect to the s-fold product e1 · · · es , see Definition 2.”