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Depth and extremal Betti number of binomial edge ideals

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  • Arvind Kumar
  • Rajib Sarkar

Abstract

Let G be a simple graph on the vertex set [n] and let JG be the corresponding binomial edge ideal. Let G=v∗H be the cone of v on H. In this article, we compute all the Betti numbers of JG in terms of the Betti numbers of JH and as a consequence, we get the Betti diagram of wheel graph. Also, we study Cohen–Macaulay defect of S/JG in terms of Cohen–Macaulay defect of SH/JH and using this we construct a graph with Cohen–Macaulay defect q for any q≥1. We obtain the depth of binomial edge ideal of join of graphs. Also, we prove that for any pair (r,b) of positive integers with 1≤b

Suggested Citation

  • 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.
    • Handle: RePEc:bla:mathna:v:293:y:2020:i:9:p:1746-1761
    DOI: 10.1002/mana.201900150
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    References listed on IDEAS

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    1. 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.
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