Regularity of symbolic powers of cover ideals of graphs

• Autores: S. A. Seyed Fakhari
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 70, Fasc. 2, 2019, págs. 187-195
• Idioma: inglés
• DOI: 10.1007/s13348-018-0228-8
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• Resumen

  • Let G be a graph which belongs to either of the following classes: (i) bipartite graphs, (ii) unmixed graphs, or (iii) claw–free graphs. Assume that J(G) is the cover ideal G and J(G)^{(k)} is its k-th symbolic power. We prove that \begin{aligned} k\mathrm{deg}(J(G))\le \mathrm{reg}(J(G)^{(k)})\le (k-1)\mathrm{deg}(J(G))+|V(G)|-1. \end{aligned} We also determine families of graphs for which the above inequalities are equality.