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Journal of Algebraic Combinatorics

, Volume 47, Issue 1, pp 17–38 | Cite as

Regularity of powers of bipartite graphs

  • A. V. Jayanthan
  • N. Narayanan
  • S. Selvaraja
Article

Abstract

Let G be a finite simple graph and I(G) denote the corresponding edge ideal. For all \(s \ge 1\), we obtain upper bounds for \({\text {reg}}(I(G)^s)\) for bipartite graphs. We then compare the properties of G and \(G'\), where \(G'\) is the graph associated with the polarization of the ideal \((I(G)^{s+1} : e_1\cdots e_s)\), where \(e_1,\cdots , e_s\) are edges of G. Using these results, we explicitly compute \({\text {reg}}(I(G)^s)\) for several subclasses of bipartite graphs.

Keywords

Bipartite graphs Castelnuovo–Mumford regularity Induced matching number Co-chordal cover number Edge ideal 

Notes

Acknowledgements

We would like to thank Adam Van Tuyl who pointed us to the article [5]. We would also like to thank Arindam Banerjee and Selvi Beyarslan for some useful discussions regarding the materials discussed in this paper. We heavily used the commutative algebra package, Macaulay 2, [13], for verifying whichever conjectures came to our mind. The third author is funded by National Board for Higher Mathematics, India.

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Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  1. 1.Department of MathematicsIndian Institute of Technology MadrasChennaiIndia

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