Characterization of Some Graphs Realizing Regularity Bounds for Binomial Edge Ideals

Nursel Erey, Muhammed Ergen, Takayuki Hibi

In this paper, we characterize all graphs $G$ satisfying \[\operatorname{reg}(S/J_G)=\ell(G)=c(G)\] where $\ell (G)$ is the sum of the lengths of the longest induced paths in each c…