An upper bound for the regularity of powers of edge ideals
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Abstract:
A recent result due to Ha and Van Tuyl proved that the Castelnuovo-Mumford regularity of the quotient ring $R/I(G)$ is at most matching number of $G$, denoted by match$(G)$. In this paper, we provide a generalization of this result for powers of edge ideals. More precisely, we show that for every graph $G$ and every $sgeq 1$, $${rm reg}( R/ I(G)^{s})leq (2s-1) |E(G)|^{s-1} {rm match}(G).$$
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Journal title
volume 43 issue 6
pages 1695- 1698
publication date 2017-11-30
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