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Paper   IPM / M / 16951
School of Mathematics
  Title:   On the depth of binomal edge ideals of graphs
  Author(s):  Sara Saeedi Madani (Joint with M. Rouzbahani and D. Kiani)
  Status:   To Appear
  Journal: J. Algebraic Combin.
  Supported by:  IPM
Let G be a graph on the vertex set [n] and JG the associated binomial edge ideal in the polynomial ring S=\KK[x1,…,xn,y1,…,yn]. In this paper we investigate the depth of binomial edge ideals. More precisely, we first establish a combinatorial lower bound for the depth of S/JG based on some graphical invariants of G. Next, we combinatorially characterize all binomial edge ideals JG with \depth S/JG=5. To achieve this goal, we associate a new poset MG with the binomial edge ideal of G, and then elaborate some topological properties of certain subposets of MG in order to compute some local cohomology modules of S/JG.

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