两类剖分图的边理想的正则度  

Regularity of Edge Ideals of Two Kinds of Partite Graphs

作　　者：朱广俊[1] 张伽祺 ZHU Guangjun;ZHANG Jiaqi(School of Mathematical Sciences,Soochow University,Suzhou Jiangsu 215006,China)

机构地区：[1]苏州大学数学科学学院,江苏苏州215006

出　　处：《大学数学》2022年第1期67-72,共6页College Mathematics

基　　金：国家自然科学基金(11271275);江苏省高等学校优势学科建设工程(80)。

摘　　要：单项式理想是多项式环中一类重要的理想,这类理想的生成元和超图的边之间可以一一对应.超图的边理想的很多代数性质和它的组合性质之间有密切的联系.根据线图、圈图和单项式理想的正则度的一些公式,通过构造合适的短正合列,给出了两类m-剖分图的边理想的正则度的精确公式,分别推广了m个顶点的线图和圈图的正则度公式.Monomial ideals are a kind of important ideals in polynomial rings.The generators of such ideals correspond to the edges of hypergraphs one by one.Many algebraic properties of the edge ideals of hypergraphs are closely related to their combinatorial properties.According to some formulas for regularity of line graphs,cycle graphs and monomial ideals,by constructing suitable short exact sequences,we provide some exact formulas for regularity for edge ideals of two kinds of m-partite graphs,which generalize the formulas for regularity of line graphs and cycle graphs with m vertices respectively.

关 键 词：线图 圈图 m-剖分图 边理想 正则度 

分 类 号：O153.3[理学—数学]