Implosive graphs: Square-free monomials on symbolic Rees algebras

Author:

Flores-Méndez A.1,Gitler I.1,Reyes E.1

Affiliation:

1. Departamento de Matemáticas, Centro de Investigación y de Estudios, Avanzados del Instituto Politécnico Nacional, Av. Instituto Politécnico Nacional No. 2508, Col. San Pedro Zacatenco, Ciudad de México, Apartado Postal 14-740, 07000 México

Abstract

Let [Formula: see text] be the edge monomial ideal of a graph [Formula: see text], whose vertex set is [Formula: see text]. [Formula: see text] is implosive if the symbolic Rees algebra [Formula: see text] of [Formula: see text] has a minimal system of generators [Formula: see text] where [Formula: see text] are square-free monomials. We give some structural properties of implosive graphs and we prove that they are closed under clique-sums and odd subdivisions. Furthermore, we prove that universally signable graphs are implosive. We show that odd holes, odd antiholes and some Truemper configurations (prisms, thetas and even wheels) are implosive. Moreover, we study excluded families of subgraphs for the class of implosive graphs. In particular, we characterize which Truemper configurations and extensions of odd holes and antiholes are minimal nonimplosive.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Algebra and Number Theory

Cited by 6 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. On the resurgence and asymptotic resurgence of homogeneous ideals;Mathematische Zeitschrift;2022-09-28

2. Regularity of symbolic powers of edge ideals;Journal of Pure and Applied Algebra;2020-07

3. Symbolic powers of edge ideals of graphs;Communications in Algebra;2020-04-07

4. Invariants of the symbolic powers of edge ideals;Journal of Algebra and Its Applications;2019-10-08

5. Ring index of a graph;Boletín de la Sociedad Matemática Mexicana;2018-02-26

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