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arXiv · 1709.03077

Regularity of symbolic powers of cover ideals of graphs

S. A. Seyed Fakhari
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Abstract

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$$k{\rm deg}(J(G))\leq {\rm reg}(J(G)^{(k)})\leq (k-1){\rm deg}(J(G))+|V(G)|-1.$$We also determine families of graphs for which the above inequalities are equality.

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S. A. Seyed Fakhari. 2017-09-10. Regularity of symbolic powers of cover ideals of graphs. https://arxiv.org/abs/1709.03077

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