Sequentially CohenMacaulay edge ideals
Authors:
Christopher A. Francisco and Adam Van Tuyl
Journal:
Proc. Amer. Math. Soc. 135 (2007), 23272337
MSC (2000):
Primary 13F55, 13D02, 05C38, 05C75
Published electronically:
March 21, 2007
MathSciNet review:
2302553
Fulltext PDF Free Access
Abstract 
References 
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Additional Information
Abstract: Let be a simple undirected graph on vertices, and let denote its associated edge ideal. We show that all chordal graphs are sequentially CohenMacaulay; our proof depends upon showing that the Alexander dual of is componentwise linear. Our result complements Faridi's theorem that the facet ideal of a simplicial tree is sequentially CohenMacaulay and implies Herzog, Hibi, and Zheng's theorem that a chordal graph is CohenMacaulay if and only if its edge ideal is unmixed. We also characterize the sequentially CohenMacaulay cycles and produce some examples of nonchordal sequentially CohenMacaulay graphs.
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Additional Information
Christopher A. Francisco
Affiliation:
Department of Mathematics, Mathematical Sciences Building, University of Missouri, Columbia, Missouri 65203
Email:
chrisf@math.missouri.edu
Adam Van Tuyl
Affiliation:
Department of Mathematical Sciences, Lakehead University, Thunder Bay, ON P7B 5E1, Canada
Email:
avantuyl@sleet.lakeheadu.ca
DOI:
http://dx.doi.org/10.1090/S0002993907088417
PII:
S 00029939(07)088417
Keywords:
Componentwise linear,
sequentially CohenMacaulay,
edge ideals,
chordal graphs
Received by editor(s):
November 1, 2005
Received by editor(s) in revised form:
April 6, 2006
Published electronically:
March 21, 2007
Communicated by:
Michael Stillman
Article copyright:
© Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
