Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2018; 55(6): 1749-1754

Online first article September 5, 2018      Printed November 30, 2018

https://doi.org/10.4134/BKMS.b171029

Copyright © The Korean Mathematical Society.

A class of edge ideals with regularity at most four

Seyed Abbas Seyedmirzaei, Siamak Yassemi

Islamic Azad (IAU), University of Tehran

Abstract

If a graph $G$ is both claw-free and gap-free, then E. Nevo showed that the Castelnuovo-Mumford regularity of the associated edge ideal $I(G)$ is at most three. Later Dao, Huneke and Schwieg gave a simpler proof of this result. In this paper we introduce a class of edge ideals with Castelnuovo-Munmford regularity at most four.

Keywords: Castelnuovo-Mumford regularity, edge ideal

MSC numbers: Primary 13D02, 13F55; Secondary 05E45

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