数学进展
數學進展
수학진전
ADVANCES IN MATHEMATICS
2004年
4期
441-446
,共6页
连通图%收缩临界连通%可收缩边%分离集%断片
連通圖%收縮臨界連通%可收縮邊%分離集%斷片
련통도%수축림계련통%가수축변%분리집%단편
connected graph%contraction-critical connected%contractible edge%separating set%fragment
Kriesell(2001年)猜想:如果κ连通图中任意两个相邻顶点的度的和至少是2[5k/4]-1,则图中有k-可收缩边.本文证明每一个收缩临界6连通图中有两个相邻的度为6的顶点,由此推出该猜想对κ=6成立.
Kriesell(2001年)猜想:如果κ連通圖中任意兩箇相鄰頂點的度的和至少是2[5k/4]-1,則圖中有k-可收縮邊.本文證明每一箇收縮臨界6連通圖中有兩箇相鄰的度為6的頂點,由此推齣該猜想對κ=6成立.
Kriesell(2001년)시상:여과κ련통도중임의량개상린정점적도적화지소시2[5k/4]-1,칙도중유k-가수축변.본문증명매일개수축림계6련통도중유량개상린적도위6적정점,유차추출해시상대κ=6성립.
Kriesell conjectured that every k connected graph has a κ-contractible edge if the degree sum of any. two adjacent vertices is at least 52[5k/4] - 1. In this note, we proved that every contraction-critical 6.connected graph contains two adjacent vertices of degree 6, so this conjecture is true for k=6.
