Regularity of Powers of Bipartite Graphs

2016/09/06 by Jayanthan, A V, Narayanan, N, Selvaraja, S
#05C25 #13D02 #13F20 #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.1609.01402

Abstract

Let G be a finite simple graph and I(G) denote the corresponding edge ideal. For all s ≥ 1, we obtain upper bounds for reg(I(G)^s) for bipartite graphs. We then compare the properties of G and G', where G' is the graph associated with the polarization of the ideal (I(G)^s+1 : e₁⋯ e_s), where e₁,… e_s are edges of G. Using these results, we explicitly compute reg(I(G)^s) for several subclasses of bipartite graphs.

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