Results 21 to 30 of about 1,118,707 (279)
Comparing powers of edge ideals [PDF]
Journal of Algebra and Its Applications, 2019 Given a nontrivial homogeneous ideal [Formula: see text], a problem of great recent interest has been the comparison of the [Formula: see text]th ordinary power of [Formula: see text] and the [Formula: see text]th symbolic power [Formula: see text]. This comparison has been undertaken directly via an exploration of which exponents [Formula: see text ...
Janssen, Mike +2 more
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Squarefree Powers of Edge Ideals of Forests [PDF]
The Electronic Journal of Combinatorics, 2021 Let $I(G)^{[k]}$ denote the $k$th squarefree power of the edge ideal of $G$. When $G$ is a forest, we provide a sharp upper bound for the regularity of $I(G)^{[k]}$ in terms of the $k$-admissable matching number of $G$. For any positive integer $k$, we classify all forests $G$ such that $I(G)^{[k]}$ has linear resolution.
Nursel Erey, Takayuki Hibi
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Induced Matchings and the v-Number of Graded Ideals
Mathematics, 2021 We give a formula for the v-number of a graded ideal that can be used to compute this number. Then, we show that for the edge ideal I(G) of a graph G, the induced matching number of G is an upper bound for the v-number of I(G) when G is very well-covered,
Gonzalo Grisalde +2 more
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Matching Numbers and Dimension of Edge Ideals [PDF]
Graphs and Combinatorics, 2021 Let $G$ be a finite simple graph on the vertex set $V(G) = \{x_{1}, \ldots, x_{n}\}$ and match$(G)$, min-match$(G)$ and ind-match$(G)$ the matching number, minimum matching number and induced matching number of $G$, respectively. Let $K[V(G)] = K[x_{1}, \ldots, x_{n}]$ denote the polynomial ring over a field $K$ and $I(G) \subset K[V(G)]$ the edge ...
Ayana Hirano, Kazunori Matsuda
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Generalization of f-Graphs and Their Algebraic Aspects
Journal of Mathematics, 2023 The notion of f-graphs and f-ideals are relatively new and have been studied in many papers. In this paper, we have generalized the idea of f-graphs and f-ideals to quasi f-graphs and quasi f-ideals, respectively. We have characterized all quasi f-graphs
Fazal Ur Rehman +3 more
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On the Linear Strand of an Edge Ideal [PDF]
Communications in Algebra, 2007 Let I(G) be the edge ideal associated to a simple graph G. We study the graded Betti numbers that appear in the linear strand of the minimal free resolution of I(G).
Roth, Mike, Van Tuyl, Adam
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Monomial s-sequences arising from graph ideals
Atti della Accademia Peloritana dei Pericolanti : Classe di Scienze Fisiche, Matematiche e Naturali, 2023 Ideals arising from graphs are investigated via s-sequence theory. In particular, the notion of s-sequence for the generators of the edge ideal I(G) of an acyclic graph G is considered for describing the Groebner basis of the relation ideal J of the ...
Maurizio Imbesi, Monica La Barbiera
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Edge ideals of oriented graphs [PDF]
International Journal of Algebra and Computation, 2019 Let [Formula: see text] be a weighted oriented graph and let [Formula: see text] be its edge ideal. Under a natural condition that the underlying (undirected) graph of [Formula: see text] contains a perfect matching consisting of leaves, we provide several equivalent conditions for the Cohen–Macaulayness of [Formula: see text].
Huy Tài Hà +4 more
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Exploring the Relationships Between Four Aging Ideals: A Bibliometric Study
Frontiers in Public Health, 2022 When examining research articles on the aging strategies, four ideals (i.e., successful aging, healthy aging, productive aging and active aging) could be explored by conducting bibliometric analyses.
Ka Lin +5 more
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Koszul Binomial Edge Ideals [PDF]
, 2014 It is shown that if the binomial edge ideal of a graph $G$ defines a Koszul algebra, then $G$ must be chordal and claw free. A converse of this statement is proved for a class of chordal and claw free graphs.
Ene, Viviana +2 more
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