On the Regularity of squarefree part of symbolic powers of edge ideals

2023/03/05 by S. A. Seyed Fakhari, Fakhari, S. A. Seyed · 2 citations
Mathematics · #Commutative Algebra and Its Applications #Rings, Modules, and Algebras #Algebraic structures and combinatorial models

paper · pdf · doi:10.48550/arxiv.2303.02791

Abstract

Assume that G is a graph with edge ideal I(G). For every integer s≥ 1, we denote the squarefree part of the s-th symbolic power of I(G) by I(G)^\s\. We determine an upper bound for the regularity of I(G)^\s\ when G is a chordal graph. If G is a Cameron-Walker graphs, we compute \rm reg(I(G)^\s\ in terms of the induced matching number of G. Moreover, for any graph G, we provide sharp upper bounds for \rm reg(I(G)^\2\) and \rm reg(I(G)^\3\).

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• Castelnuovo-Mumford Regularity and Combinatorial Invariants of Trees
• Admissible set and squarefree-power-like function with applications to squarefree symbolic powers

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