Characterization of Some Graphs Realizing Regularity Bounds for Binomial Edge Ideals
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2026
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866908817789288448 |
|---|---|
| author | Erey, Nursel Ergen, Muhammed Hibi, Takayuki |
| author_facet | Erey, Nursel Ergen, Muhammed Hibi, Takayuki |
| contents | 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 \[\operatorname{reg}(S/J_G)=\ell(G)=|V(G)|-ω(G)+1\] where $ω(G)$ 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 $[\ell(G), |V(G)|-ω(G)+1]$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_06524 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Characterization of Some Graphs Realizing Regularity Bounds for Binomial Edge Ideals Erey, Nursel Ergen, Muhammed Hibi, Takayuki Commutative Algebra Combinatorics 05E40, 13D02, 05C75 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 \[\operatorname{reg}(S/J_G)=\ell(G)=|V(G)|-ω(G)+1\] where $ω(G)$ 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 $[\ell(G), |V(G)|-ω(G)+1]$. |
| title | Characterization of Some Graphs Realizing Regularity Bounds for Binomial Edge Ideals |
| topic | Commutative Algebra Combinatorics 05E40, 13D02, 05C75 |
| url | https://arxiv.org/abs/2602.06524 |