On the index of powers of edge ideals

Abstract

The index of a graded ideal measures the number of linear steps in the graded minimal free resolution of the ideal. In this paper we study the index of powers and squarefree powers of edge ideals. Our results indicate that the index as a function of the power of an edge ideal $I$ is strictly increasing if $I$ has linear relations. Examples show that this need not to be the case for monomial ideals generated in degree greater than two.

21 pages, 1 figure

Cited by in corpus (4)

• On squarefree powers of simplicial trees
• The Scarf complex of squarefree powers, symbolic powers of edge ideals, and cover ideals of graphs
• Square-free powers of Cohen-Macaulay simplicial forests
• Linear syzygy graph and linear resolution