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Cohen-Macaulay edge ideal whose height is half of the number of vertices

Published online by Cambridge University Press:  11 January 2016

Marilena Crupi ,
Giancarlo Rinaldo  and
Naoki Terai
Marilena Crupi
Affiliation:
Dipartimento di Matematica Università di Messina, 98166 Messina, Italy, mcrupi@unime.it
Giancarlo Rinaldo
Affiliation:
Dipartimento di Matematica Università di Messina, 98166 Messina, Italy, rinaldo@dipmat.unime.it
Naoki Terai
Affiliation:
Department of Mathematics Faculty of Culture and Education Saga University, Saga 840-8502, Japan, terai@cc.saga-u.ac.jp
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Abstract

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We consider a class of graphs G such that the height of the edge ideal I(G) is half of the number #V(G) of the vertices. We give Cohen-Macaulay criteria for such graphs.

Keywords

05C7505C9013H1055U10
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 201 , March 2011 , pp. 117 - 131
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2011

References

[1] Bruns, W. and Herzog, J., Cohen-Macaulay rings, Cambridge Univ. Press, Cambridge, 1997.Google Scholar
[2] Diestel, R., Graph Theory, 2nd ed., Grad. Texts in Math. 173, Springer, Berlin, 2000.Google Scholar
[3] Estrada, M. and Villarreal, R. H., Cohen-Macaulay bipartite graphs, Arch. Math. (Basel) 68 (1997), 124–128.Google Scholar
[4] Faridi, S., “Cohen-Macaulay properties of square-free monomial ideals” in Commutative Algebra, Lect. Notes Pure Appl. Math. 244, Chapman & Hall, Boca Raton, Fla, 2006, 85–114.Google Scholar
[5] Gitler, I. and Valencia, C. E., Bounds for invariants of edge-rings, Comm. Algebra 33 (2005), 1603–1616.Google Scholar
[6] Gitler, I. and Valencia, C. E., Bounds for graph invariants, preprint, arXive:math/0510387v2 [math.CO] Google Scholar
[7] Haghighi, H., Yassemi, S., and Zaare-Nahandi, R., Bipartite S2 graphs are Cohen-Macaulay, to appear in Bull. Math. Soc. Sci. Math. Roumanie (N.S.).Google Scholar
[8] Herzog, J. and Hibi, T., Distributive lattices, bipartite graphs and Alexander duality, J. Algebraic Combin. 22 (2005), 289–302.Google Scholar
[9] Herzog, J., Hibi, T., and Zheng, X., The monomial ideal of a finite meet-semilattice, Trans. Amer. Math. Soc. 358 (2006), 4119–4134.CrossRefGoogle Scholar
[10] Morey, S., Reyes, E., and Villarreal, R. H., Cohen-Macaulay, shellable and unmixed clutters with a perfect matching of König type, J. Pure Appl. Algebra 212 (2008), 1770–1786.Google Scholar
[11] Stückrad, J. and Vogel, W., Buchsbaum Rings and Applications: An Interaction between Algebra, Geometry and Topology, Springer, Berlin, 1986.Google Scholar
[12] Van Tuyl, A. and Villarreal, R. H., Shellable graphs and sequentially Cohen-Macaulay bipartite graphs, J. Combin. Theory Ser. A 115 (2008), 779–814.Google Scholar
[13] Villarreal, R. H., Monomial Algebras, Monogr. Textbooks Pure Appl. Math. 238, Marcel Dekker, New York, 2001.Google Scholar
[14] Villarreal, R. H., Unmixed bipartite graphs, Rev. Colombiana Mat. 41 (2007), 393–395.Google Scholar