Binomial Edge Ideals of Graphs

  • Dariush Kiani
  • Sara Saeedi
Keywords: Binomial edge ideals, Linear resolutions, Castelnuovo-Mumford regularity


We characterize all graphs whose binomial edge ideals have a linear resolution. Indeed, we show that complete graphs are the only graphs with this property. We also compute some graded components of the first Betti number of the binomial edge ideal of a graph with respect to the graphical terms. Finally, we give an upper bound for the Castelnuovo-Mumford regularity of the binomial edge ideal of a closed graph.

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