An upper bound for the regularity of powers of edge ideals

author

  • M. Moghimian Department of Mathematics‎, ‎Science and Research Branch‎, ‎Islamic Azad University (IAU)‎, ‎Tehran‎, ‎Iran.
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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