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Minimal Reductions and Cores of Edge Ideals
edge ideal even cycles minimal reductions core
2011/2/28
We study minimal reductions of edge ideals of graphs containing a unique even cycle, and determine restrictions on the coefficients of the generators of these minimal reductions.
Edge ideals: algebraic and combinatorial properties
Edge ideal regularity associated prime sequentially Cohen-Macaulay
2011/2/25
Let C be a clutter and let I(C) R be its edge ideal. This is a survey paper on
the algebraic and combinatorial properties of R/I(C) and C, respectively. We give a criterion to estimate the regulari...
Given an edge ideal of graph G, we show that if the first nonlinear strand in the resolution of IG is zero until homological stage a1, then the next non-linear strand in the resolution is zero until h...
Betti numbers of edge ideals of uniform hypergraphs
Betti number hypergraph Hilbert function Stanley-Reisner ring
2010/11/29
We describe the Betti numbers of the edge ideals I(G) of uniform hypergraphs G such that I(G) has linear graded free resolution.