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On the extremal Betti numbers of the binomial edge ideal of closed graphs

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  • Hernán de Alba
  • Do Trong Hoang

Abstract

We study the equality of the extremal Betti numbers of the binomial edge ideal JG and those of its initial ideal in (JG) for a closed graph G. We prove that in some cases there is a unique extremal Betti number for in (JG) and as a consequence there is a unique extremal Betti number for JG and these extremal Betti numbers are equal.

Suggested Citation

  • Hernán de Alba & Do Trong Hoang, 2018. "On the extremal Betti numbers of the binomial edge ideal of closed graphs," Mathematische Nachrichten, Wiley Blackwell, vol. 291(1), pages 28-40, January.
    • Handle: RePEc:bla:mathna:v:291:y:2018:i:1:p:28-40
    DOI: 10.1002/mana.201700292
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    Cited by:

    1. René González‐Martínez, 2021. "Gorenstein binomial edge ideals," Mathematische Nachrichten, Wiley Blackwell, vol. 294(10), pages 1889-1898, October.
    2. Arvind Kumar & Rajib Sarkar, 2020. "Depth and extremal Betti number of binomial edge ideals," Mathematische Nachrichten, Wiley Blackwell, vol. 293(9), pages 1746-1761, September.
    3. Sara Saeedi Madani & Dariush Kiani, 2021. "Induced matchings in strongly biconvex graphs and some algebraic applications," Mathematische Nachrichten, Wiley Blackwell, vol. 294(6), pages 1160-1174, June.

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