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Journal of Algebraic Combinatorics

, Volume 43, Issue 2, pp 325–338 | Cite as

A characterization of triangle-free Gorenstein graphs and Cohen–Macaulayness of second powers of edge ideals

Article

Abstract

We graph-theoretically characterize triangle-free Gorenstein graphs G. As an application, we classify when \(I(G)^2\) is Cohen–Macaulay.

Keywords

Graph Triangle-free Well-covered Edge ideal Cohen–Macaulay Gorenstein 

Mathematics Subject Classification

13D45 05C90 05E40 05E45 

Notes

Acknowledgments

We would like to thank Professors L. T. Hoa and N. V. Trung for helpful comments. Part of this work was done while we were at the Vietnam Institute of Advanced Studies in Mathematics (VIASM) in Hanoi, Vietnam. We would like to thank VIASM for its hospitality. We would also like to thank the anonymous referees for many helpful comments.

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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Institute of MathematicsVASTHanoiViet Nam

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