Regularity of powers of forests and cycles
Commutative Algebra
2022-09-30 v2 Combinatorics
Abstract
Let G be a graph and let I = I(G) be its edge ideal. In this paper, when G is a forest or a cycle, we explicitly compute the regularity of I^s for all s > 0. In particular, for these classes of graphs, we provide the asymptotic linear function reg(I^s) as s > 0, and the initial value of s starting from which reg(I^s) attains its linear form. We also give new bounds on the regularity of I when G contains a Hamiltonian path and when G is a Hamiltonian graph.
Cite
@article{arxiv.1409.0277,
title = {Regularity of powers of forests and cycles},
author = {Selvi Kara and Huy Tai Ha and Tran Nam Trung},
journal= {arXiv preprint arXiv:1409.0277},
year = {2022}
}
Comments
Changed title, 16 pages, 3 figures