Let G be a finite simple graph and I(G) denote the corresponding edge ideal. For all s≥1\documentclass[12pt]{minimal}
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\begin{document}$$s \ge 1$$\end{document}, we obtain upper bounds for reg(I(G)s)\documentclass[12pt]{minimal}
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\begin{document}$${\text {reg}}(I(G)^s)$$\end{document} for bipartite graphs. We then compare the properties of G and G′\documentclass[12pt]{minimal}
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\begin{document}$$G'$$\end{document}, where G′\documentclass[12pt]{minimal}
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\begin{document}$$G'$$\end{document} is the graph associated with the polarization of the ideal (I(G)s+1:e1⋯es)\documentclass[12pt]{minimal}
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\begin{document}$$(I(G)^{s+1} : e_1\cdots e_s)$$\end{document}, where e1,⋯,es\documentclass[12pt]{minimal}
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\begin{document}$$e_1,\cdots , e_s$$\end{document} are edges of G. Using these results, we explicitly compute reg(I(G)s)\documentclass[12pt]{minimal}
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\begin{document}$${\text {reg}}(I(G)^s)$$\end{document} for several subclasses of bipartite graphs.
