The Castelnuovo-Mumford regularity of binomial edge ideals

详细信息    查看全文

• 作者：Dariush Kiani^a ; ^b ; ^{dkiani@aut.ac.ir" class="auth_mail" title="E-mail the corresponding author} ; ^{dkiani7@gmail.com" class="auth_mail" title="E-mail the corresponding author} ; Sara Saeedi Madani^c ; ^{sara.saeedimadani@uni-osnabrueck.de" class="auth_mail" title="E-mail the corresponding author} ; ^{sarasaeedim@gmail.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Binomial edge ideal ; Castelnuovo&ndash ; Mumford regularity ; Simplicial vertex
• 刊名：Journal of Combinatorial Theory, Series A
• 出版年：2016
• 出版时间：April 2016
• 年：2016
• 卷：139
• 期：Complete
• 页码：80-86
• 全文大小：269 K

文摘

We prove a conjectured upper bound for the Castelnuovo–Mumford regularity of binomial edge ideals of graphs, due to Matsuda and Murai. Indeed, we prove that reg(J_G)≤n−1$\mathrm{reg}(J_G)\le n-1$ for any graph G with n vertices, which is not a path.