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Regularity of symbolic powers of complementary edge ideals
Abstract
Let G be a finite simple graph on n vertices, and let Ic(G) be its complementary edge ideal. We determine reg(Ic(G)(t)) for every t≥1 in terms of the number c(G) of nontrivial connected components of G and the presence of a K2-component. Consequently, reg(Ic(G)(t))≤ reg(Ic(G)t) for all t≥1, with equality for every t if and only if either c(G)=1, or c(G)=2 and G has a K2-component. We also characterize Serre's condition (S2) for R/Ic(G), and classify the graphs for which R/Ic(G)(t) is Cohen-Macaulay for every t≥1.
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BibTeX
@misc{hien2026regularity,
title = {{Regularity of symbolic powers of complementary edge ideals}},
author = {Truong Thi Hien and Manohar Kumar},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.06903},
eprint = {2609.06903},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.06903},
}
RIS
TY - UNPB
TI - Regularity of symbolic powers of complementary edge ideals
AU - Truong Thi Hien
AU - Manohar Kumar
PY - 2026
DA - 2026/09/07
PB - arXiv
DO - 10.48550/arxiv.2609.06903
UR - https://arxiv.org/abs/2609.06903
AB - Let G be a finite simple graph on n vertices, and let I_c(G) be its complementary edge ideal. We determine reg(I_c(G)^(t)) for every t≥1 in terms of the number c(G) of nontrivial connected components of G and the presence of a K_2-component. Consequently, reg(I_c(G)^(t))≤ reg(I_c(G)^t) for all t≥1, with equality for every t if and only if either c(G)=1, or c(G)=2 and G has a K_2-component. We also characterize Serre's condition (S_2) for R/I_c(G), and classify the graphs for which R/I_c(G)^(t) is Cohen-Macaulay for every t≥1.
ER -