Linear quotients of connected ideals of graphs
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866917972612743168 |
|---|---|
| author | Ananthnarayan, H. Javadekar, Omkar Maithani, Aryaman |
| author_facet | Ananthnarayan, H. Javadekar, Omkar Maithani, Aryaman |
| contents | As a higher analogue of the edge ideal of a graph, we study the $t$-connected ideal $\operatorname{J}_{t}$. This is the monomial ideal generated by the connected subsets of size $t$. For chordal graphs, we show that $\operatorname{J}_{t}$ has a linear resolution iff the tree is $t$-gap-free, and that this is equivalent to having linear quotients. We then show that if $G$ is any gap-free and $t$-claw-free graph, then $\operatorname{J}_{t}(G)$ has linear quotients and, hence, linear resolution. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_01046 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Linear quotients of connected ideals of graphs Ananthnarayan, H. Javadekar, Omkar Maithani, Aryaman Commutative Algebra Combinatorics 13F55, 13D02, 05E40 As a higher analogue of the edge ideal of a graph, we study the $t$-connected ideal $\operatorname{J}_{t}$. This is the monomial ideal generated by the connected subsets of size $t$. For chordal graphs, we show that $\operatorname{J}_{t}$ has a linear resolution iff the tree is $t$-gap-free, and that this is equivalent to having linear quotients. We then show that if $G$ is any gap-free and $t$-claw-free graph, then $\operatorname{J}_{t}(G)$ has linear quotients and, hence, linear resolution. |
| title | Linear quotients of connected ideals of graphs |
| topic | Commutative Algebra Combinatorics 13F55, 13D02, 05E40 |
| url | https://arxiv.org/abs/2401.01046 |