| Autor: |
Bolognini, Davide, Macchia, Antonio, Rinaldo, Giancarlo, Strazzanti, Francesco |
| Rok vydání: |
2022 |
| Předmět: |
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| Druh dokumentu: |
Working Paper |
| Popis: |
A combinatorial property that characterizes Cohen-Macaulay binomial edge ideals has long been elusive. A recent conjecture ties the Cohen-Macaulayness of a binomial edge ideal $J_G$ to special disconnecting sets of vertices of its underlying graph $G$, called \textit{cut sets}. More precisely, the conjecture states that $J_G$ is Cohen-Macaulay if and only if $J_G$ is unmixed and the collection of the cut sets of $G$ is an accessible set system. In this paper we prove the conjecture theoretically for all graphs with up to $12$ vertices and develop an algorithm that allows to computationally check the conjecture for all graphs with up to $15$ vertices and all blocks with whiskers where the block has at most $11$ vertices. This significantly extends previous computational results. |
| Databáze: |
arXiv |
| Externí odkaz: |
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