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REGULARITY OF POWERS OF BIPARTITE GRAPHS

Part of: Algebraic combinatorics Theory of modules and ideals Commutative algebra: Homological methods

Published online by Cambridge University Press:  19 September 2022

AJAY KUMAR  and
RAJIV KUMAR
AJAY KUMAR*
Affiliation:
Department of Mathematics, Indian Institute of Technology Jammu, Jammu, India
RAJIV KUMAR
Affiliation:
Department of Mathematics, Indian Institute of Technology Jammu, Jammu, India e-mail: gargrajiv00@gmail.com
*
e-mail: ajay.kumar@iitjammu.ac.in
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Abstract

For a simple bipartite graph G, we give an upper bound for the regularity of powers of the edge ideal $I(G)$ in terms of its vertex domination number. Consequently, we explicitly compute the regularity of powers of the edge ideal of a bipartite Kneser graph. Further, we compute the induced matching number of a bipartite Kneser graph.

Keywords

regularitybipartite Kneser graphedge idealvertex domination number

MSC classification

Primary: 05E40: Combinatorial aspects of commutative algebra
Secondary: 13C14: Cohen-Macaulay modules 13D02: Syzygies, resolutions, complexes
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 107 , Issue 1 , February 2023 , pp. 1 - 9
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Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.

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