التفاصيل البيبلوغرافية
| العنوان: |
Cohen-Macaulay binomial edge ideals of small graphs |
| المؤلفون: |
Bolognini, Davide, Macchia, Antonio, Rinaldo, Giancarlo, Strazzanti, Francesco |
| سنة النشر: |
2022 |
| المجموعة: |
Mathematics |
| مصطلحات موضوعية: |
Mathematics - Commutative Algebra, Mathematics - Combinatorics |
| الوصف: |
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. |
| نوع الوثيقة: |
Working Paper |
| URL الوصول: |
http://arxiv.org/abs/2212.09181 |
| رقم الانضمام: |
edsarx.2212.09181 |
| قاعدة البيانات: |
arXiv |