Regularity of powers of bipartite graphs

By A. V. Jayanthan, And N. NARAYANAN, S. Selvaraja. Journal of Algebraic Combinatorics, 2016

75 citations recorded by the source corpus.

Let G be a finite simple graph and I(G) denote the corresponding edge ideal. For all s≥1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$s \ge 1$$\end{document}, we obtain upper bounds for reg(I(G)s)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text {reg}}(I(G)^s)$$\end{document} for bipartite graphs. We then compare the properties of G and G′\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$G'$$\end{document}, where G′\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$G'$$\end{document} is the graph associated with the polarization of the ideal (I(G)s+1:e1⋯es)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(I(G)^{s+1} : e_1\cdots e_s)$$\end{document}, where e1,⋯,es\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$e_1,\cdots , e_s$$\end{document} are edges of G. Using these results, we explicitly compute reg(I(G)s)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text {reg}}(I(G)^s)$$\end{document} for several subclasses of bipartite graphs.

Subfields: Algebra and Number Theory, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/86a0d6ecfcb9f64ef5bfae6f6ae01c8bdec07435

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In Algebra and Number Theory

  1. Arindam Banerjee
  2. Huy Tài Hà
  3. Selvi Kara
  4. Adam Van Tuyl
  5. Tran Nam Trung
  6. S. Beyarslan
  7. K. Kimura
  8. A. Alilooee

In Geometry and Topology

  1. Arindam Banerjee
  2. Selvi Kara
  3. Huy Tài Hà
  4. Adam Van Tuyl
  5. K. Kimura
  6. Tran Nam Trung
  7. S. Beyarslan

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