Bounds on the regularity of toric ideals of graphs

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• 作者：Jennifer Biermann^a ; ^{biermann@hws.edu} ; Augustine O'Keefe^b ; ^{aokeefe@conncoll.edu} ; Adam Van Tuyl^c ; ^{vantuyl@math.mcmaster.ca}
• 关键词：14M25 ; 13D02 ; 05E40 ; 52B22
• 刊名：Advances in Applied Mathematics
• 出版年：2017
• 出版时间：April 2017
• 年：2017
• 卷：85
• 期：Complete
• 页码：84-102
• 全文大小：466 K
• 卷排序：85

文摘

Let G   be a finite simple graph. We give a lower bound for the Castelnuovo–Mumford regularity of the toric ideal IGIG associated to G in terms of the sizes and number of induced complete bipartite graphs in G. When G   is a chordal bipartite graph, we find an upper bound for the regularity of IGIG in terms of the size of the bipartition of G  . We also give a new proof for the graded Betti numbers of the toric ideal associated to the complete bipartite graph K2,nK2,n.