Let I and J be edge ideals in a polynomial ring R = K[x 1 ,. .. , x n ] with I ⊆ J. In this paper... more Let I and J be edge ideals in a polynomial ring R = K[x 1 ,. .. , x n ] with I ⊆ J. In this paper, we obtain a general upper and lower bound for the Castelnuovo-Mumford regularity of IJ in terms of certain invariants associated with I and J. Using these results, we explicitly compute the regularity of IJ for several classes of edge ideals. In particular, we compute the regularity of IJ when J has linear resolution. Finally, we compute the precise expression for the regularity of J 1 J 2 • • • J d , d ∈ {3, 4}, where J 1 ,. .. , J d are edge ideals, J 1 ⊆ J 2 ⊆ • • • ⊆ J d and J d is the edge ideal of a complete graph.
Let I and J be edge ideals in a polynomial ring R = K[x 1 ,. .. , x n ] with I ⊆ J. In this paper... more Let I and J be edge ideals in a polynomial ring R = K[x 1 ,. .. , x n ] with I ⊆ J. In this paper, we obtain a general upper and lower bound for the Castelnuovo-Mumford regularity of IJ in terms of certain invariants associated with I and J. Using these results, we explicitly compute the regularity of IJ for several classes of edge ideals. In particular, we compute the regularity of IJ when J has linear resolution. Finally, we compute the precise expression for the regularity of J 1 J 2 • • • J d , d ∈ {3, 4}, where J 1 ,. .. , J d are edge ideals, J 1 ⊆ J 2 ⊆ • • • ⊆ J d and J d is the edge ideal of a complete graph.
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