Gapfree graphs and powers of edge ideals with linear quotients
| Autor: | Erey, Nursel, Faridi, Sara, Hà, Tài Huy, Hibi, Takayuki, Kara, Selvi, Morey, Susan |
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| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | Let $G$ be a gapfree graph and let $I(G)$ be its edge ideal. An open conjecture of Nevo and Peeva states that $I(G)^q$ has a linear resolution for $q\gg 0$. We investigate a stronger conjecture that if $I(G)^q$ has linear quotients for some integer $q$, then $I(G)^{q+1}$ also has linear quotients. We give a partial solution to this conjecture. It is known that if $G$ does not contain a cricket, a diamond, or a $C_4$, then $I(G)^q$ has a linear resolution for $q \geq 2$. We construct a family of gapfree graphs $G$ containing cricket, diamond, $C_4$ and $C_5$ as induced subgraphs of $G$ for which $I(G)^q$ has linear quotients for $q \ge 2$. Comment: 26 pages, 5 figures |
| Databáze: | arXiv |
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