简约极小3连通图非基本边的分布

Distribution of Non-Essential Edges in ReducedMinimally 3-Connected Graphs

通过分析简约极小3连通图G的非基本边的分布规律,得出:G中没有连续相邻的5条基本边;G的每一个圈C上至少有15C条非基本边。并由此得到,G的每一棵非平凡生成树上至少有一条非基本边。

The distribution of non-essential edges in reduced minimally 3-connected graphs is discussed in this paper.The following results are obtained:No five consecutive edges of G * are essental edge;Each cycle C of G * contains at least GFDB2%15CGFDB3%non-essential edges,and thus there is at least one non-essential edge in non-trivial spanning tree of G *.