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Regularity of powers of forests and cycles

Research paper by Selvi Beyarslan, Huy Tài Hà, Trân Nam Trung

Indexed on: 14 Jul '15Published on: 14 Jul '15Published in: Journal of Algebraic 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 \(s \ge 1\). In particular, for these classes of graphs, we provide the asymptotic linear function \({{\mathrm{reg}}}(I^s)\) as \(s \gg 0\), and the initial value of s starting from which \({{\mathrm{reg}}}(I^s)\) 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.