收缩临界5连通图中5度点的分布

The Distribution of Vertices of Degree 5 in Contraction Critical 5-Connected Graphs

关键词:  5连通图  收缩临界  断片

Key words:  5-connected graphs  contraction critical  fragment

摘要:

当G是收缩临界5连通图,x∈V(G)且d(x)≥ 6,x₁,x₂为与x相邻的5度点时,证明如果x₁x₂∈E(G),则x与3个5度点相邻.

Abstract:

Let G be a contraction critical 5-connected graph, x∈V (G), d (x) ≥ 6 and x₁, x₂∈N (x)∩V₅(G).If x₁x₂∈E (G), then there exist 3 vertices of degree 5 in the neighborhood of x.