摘要
定义了一类极大外平面图 :(r,k)—扇 .证明了当G是以r个顶点的圈Qr 为标定界环的 (r,k)—扇 ,G′是以Qr 为标定界环的任意极大外平面图时 ,G和G′有公共四染色 ;同时对△ (G) =r- 3的极大外平面图也得到相同的结论 .从而证明了四色定理的等价命题在给定条件下成立 .
The defination of (r,k)-fan is given. It is proved that when G is an (r,k)-fan with labeled boundary circuit Q r and G′ is any maximal outerplanar graph with the same boundary circuit Q r then G and G′ have a common 4-colouring. When G is a maximal outerplanar graph with labeled boundary circuit Q r and △(G)=r-3,the same result is given. Therefore the corresponding proposition of the four colour conjecture is proved under the given conditions
出处
《数学研究》
CSCD
2001年第4期406-410,共5页
Journal of Mathematical Study
基金
国家攀登计划资助
编号 970 2 110 17
关键词
极大外平面图
扇
染色
四色定理
连通图
maximal outerplanar graph
colouring
(r,k)-fan,four colour conjecture
