中文摘要：

M．Kriesell证明了收缩临界5-连通图的平均度不超过24并猜想收缩临界5-连通图的平均度小于10．本文构造了一个反例证明M．Kriesell的猜想不成立并给出了收缩临界5-连通图平均度新的上界．

英文摘要：

M. Kriesell shown that any contraction critical 5-connected graph has average degree at most 24 and conjectured that every finite 5-connected graph of average degree at least 10 admitted an 5-contractible edge. We show this Conjecture is not true by giving a counter example. Further we show that any finite contraction critical 5-connected graph has average degree at most 20. This improve the result of M. Kriesell.