{nest,gap}-free图的边理想正则度的研究

Regularity of edge ideals of {nest,gap}-free graphs

gap-free图是指不含gap作为导出子图的图,其中gap是顶点集为{a,b,u,v}和边集为{ab,uv}的图.证明了所有的nest-free且gap-free图的边理想正则度reg I((G))是小于等于3的.定义了n-gap-free图,并刻画了一些n-gap-free图的边理想的正则度.

Gap-free graph is a class of graph which is not contain a gap as derived subgraph,in which a gap is the graph with vertex set {a,b,u,v} and edge set {ab,uv}.In the report,if G is {nest,gap}-free graph,reg(I(G)) ≤ 3 is proved.n-gap-free graph is defined,and the regularity of the edge ideals of some n-gap-free graphs is characterized.