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 e-prints
- 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
- E-Print:
- Changed title, 16 pages, 3 figures