Using polyhedral geometry and integral closure, we give necessary conditions for the equality of ordinary and symbolic powers of monomial ideals with a minimal irreducible decomposition. Then, we classify when the Alexander dual of the edge ideal of a weighted oriented graph is normally torsion-free...
test .JuliaFormatter.toml .gitignore CITATION.bib LICENSE.md Project.toml README.md SimpleWeightedGraphs Edge-weighted graphs compatible withGraphs.jl. See thedocumentationfor a tutorial. Releases4 v1.5.0Latest Mar 13, 2025 + 3 releases
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If each of the edges bears the weight 1, i.e., the function f(x,y)≡1, then the adjacency matrix of G is simply denoted by A(G). Because we study the interlacing results of weighted adjacency eigenvalues under some graph perturbations, firstly, we define some operations on graphs. ...
For graphs with integer weights, shortest paths can be found in linear time, on the RAM model using the algorithm of Thorup [12]. For planar graphs, the algorithm of Henzinger et al. [3] can be used instead. As part of preprocessing, we first carry out preorder traversal on our ...
Also, we prove that ifis a weighted oriented graph andw(x)>1for allx鈭圴(), thenI()has a linear resolution if and only if all powers ofI()have linear quotients. We provide a lower bound for the regularity of powers of edge ideals of weighted oriented graphs in terms of induced ...
The sequentially Cohen-Macaulay property of edge ideals of edge-weighted graphsSequentially Cohen-MacaulayEdge-weighted graphMonomial idealSHELLABLE NONPURE COMPLEXESOBSTRUCTIONSLet I(G,w)documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} use...
and only if all powers ofI(D)I(𝒟)have linear quotients. We provide a lower bound for the regularity of powers of edge ideals of weighted oriented graphs in terms of induced matching. Finally, we obtain a general upper bound for the regularity of edge ideals of weighted oriented graphs....
4, 1672鈥 1685) classified all edge ideals of weighted oriented graphs for which the symbolic and ordinary powers coincide. In this article, we explore the same question under the second definition of symbolic powers. Let D \\mathcal {D} be a weighted oriented graph, and let I ( D ) ...
Weighted oriented graphSink vertexEdge idealSymbolic powerInduced odd cycleEven cycleStar graphLet D D be a weighted oriented graph and I(D) I(D) be its edge ideal. We provide one method to find all the minimal generators of I_{\\subseteq C} I_{\\subseteq C} , where C C is a ...