Regularity of powers of forests and cycles
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.
 Publication:

arXiv eprints
 Pub Date:
 August 2014
 DOI:
 10.48550/arXiv.1409.0277
 arXiv:
 arXiv:1409.0277
 Bibcode:
 2014arXiv1409.0277K
 Keywords:

 Mathematics  Commutative Algebra;
 Mathematics  Combinatorics;
 13D45;
 05C38
 EPrint:
 Changed title, 16 pages, 3 figures