Symbolic powers of certain cover ideals of graphs

Kumar, Arvind; Kumar, Rajiv; Sarkar, Rajib; Selvaraja, S.

doi:10.48550/arxiv.1903.00178

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Conjecture 11 Let G Be a Chordal Graph Then Powers Of The Co...1

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2021

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“…Although the constant a is given by the maximum degree of minimal generators of I, no explicit formula for b and s 0 is known. The problem of computing the bounds for the regularity of (symbolic) powers of the vertex cover ideal of a graph has been studied by many researchers (see [6,14,19,20,21]).…”

Section: Conjecture 11 Let G Be a Chordal Graph Then Powers Of The Co...mentioning

confidence: 99%

Symbolic Powers of Certain Cover Ideals of Graphs

Kumar

Sarkar

et al. 2021

Acta Math Vietnam

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Let S = k[x 1 , . . . , x n ] be a polynomial ring, where k is a field, and G be a simple graph on n vertices. Let J(G) ⊂ S be the cover ideal of G. In this article, we solve a conjecture due to Herzog, Hibi and Ohsugi for trees which states that powers of cover ideals of trees are componentwise linear. Also, we show that if G is a unicyclic vertex decomposable graph unless it contains C 3 or C 5 , then symbolic powers of J(G) are componentwise linear.

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Section: Conjecture 11 Let G Be a Chordal Graph Then Powers Of The Co...mentioning

confidence: 99%