中文摘要：

图的覆盖问题是图论研究的一个主要内容.若图G的每个极小H-覆盖都是它的最小H-覆盖,则称图G为H-等可覆盖的.为刻画M 2-等可覆盖图的特征,采用分类讨论的方法,得出M 2-等可覆盖图的一个重要结果：若连通图G含6圈,则G不是M 2-等可覆盖的.这为M 2-等可覆盖图的完全刻画奠定了有力的基础.

英文摘要：

Covering of graphs is a main content of graph theory.A graph G is called H-equicoverable if every minimal H-covering in G is also a minimum H-covering in G.To give the characterization of M 2-equicoverable graphs,an important result for connected M 2-equicoverable graphs is obtained by using the method of case by case：if G is a connected graph that contains a 6-cycle,then G is not M 2-equicoverable.This result provides a strong base for en-tirely characterizing all M 2-equicoverable graphs.