An upper bound for the regularity of powers of edge ideals

Document Type: Research Paper

Author

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 $s\geq 1$‎, ‎$${\rm reg}( R‎/ ‎I(G)^{s})\leq (2s-1) |E(G)|^{s-1} {\rm match}(G).$$‎

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Volume 43, Issue 6
November and December 2017
Pages 1695-1698
  • Receive Date: 09 June 2016
  • Revise Date: 12 September 2016
  • Accept Date: 12 September 2016