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Characterization of Some Graphs Realizing Regularity Bounds for Binomial Edge Ideals
Nursel Erey, Muhammed Ergen, Takayuki Hibi
https://arxiv.org/abs/2602.06524 https://arxiv.org/pdf/2602.06524 https://arxiv.org/html/2602.06524
arXiv:2602.06524v1 Announce Type: new
Abstract: 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 connected component of $G$ and $c(G)$ is the number of the maximal cliques of $G$. We also characterize all connected graphs $G$ that satisfy \[\operatorname{reg}(S/J_G)=\ell(G)=|V(G)|-\omega(G) 1\] where $\omega(G)$ is the clique number of $G$. Moreover, we investigate the possible values of the regularity of $S/J_G$ within the intervals $[\ell(G), c(G)]$ and $[\ell(G), |V(G)|-\omega(G) 1]$.
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Replaced article(s) found for cond-mat.mes-hall. https://arxiv.org/list/cond-mat.mes-hall/new
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