数学研究
數學研究
수학연구
JOURNAL OF MATHEMATICAL STUDY
2011年
3期
243-256
,共14页
5-连通图%收缩临界%平均度
5-連通圖%收縮臨界%平均度
5-련통도%수축림계%평균도
5-connected graph%contraction critical%average degree
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．
M．Kriesell證明瞭收縮臨界5-連通圖的平均度不超過24併猜想收縮臨界5-連通圖的平均度小于10．本文構造瞭一箇反例證明M．Kriesell的猜想不成立併給齣瞭收縮臨界5-連通圖平均度新的上界．
M．Kriesell증명료수축림계5-련통도적평균도불초과24병시상수축림계5-련통도적평균도소우10．본문구조료일개반예증명M．Kriesell적시상불성립병급출료수축림계5-련통도평균도신적상계．
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.
