Depth and extremal Betti number of binomial edge ideals

Arvind Kumar and Rajib Sarkar

Mathematische Nachrichten, 2020, vol. 293, issue 9, 1746-1761

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

Date: 2020
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