赋权图过指定点的圈  

Large cycles passing through a specified vertex in weighted graphs

作　　者：卞秋香[1] 孙志人[2] 

机构地区：[1]江苏科技大学数理学院,江苏镇江212003 [2]南京师范大学数学与计算机科学学院,江苏南京210097

出　　处：《河海大学学报（自然科学版）》2005年第6期721-724,共4页Journal of Hohai University(Natural Sciences)

摘　　要：设G是满足条件D1和D2的2-连通非Hamilton赋权图,证明了如下新结果:若G满足dw(x)+dw(y)≥m(xy E(G),x≠y),则通过图G的每个顶点存在权重大于或等于m的圈.该结果推广了非赋权图的已有结果.Under the assumption that G is a 2-connected non-Hamilton weighted graph satisfying conditions D1 and D2, a new conclusion is verified： if G satisfies d^w（ x ） ＋ d^w（ y ） ≥ m（ xy 不属于 E（G）, x ≠ y ）, through each vertex of graph G, there exist cycles with the weight equal to or greater than m. The conclusion extends Enomoto＇ s theorem for the unweighted graphs to the weighted graphs.

关 键 词：赋权图 赋权度 HAMILTON圈 

分 类 号：O157.5[理学—数学]