华东师范大学学报(自然科学版) ›› 2006, Vol. 2006 ›› Issue (5): 76-82.

• 数学 统计学 • 上一篇    下一篇

几类图的最优填充数

汤洁泉, 束金龙   

  1. 华东师范大学 数学系, 上海 200062
  • 收稿日期:2005-01-17 修回日期:2005-04-20 出版日期:2006-09-25 发布日期:2012-11-27

Fill-in Numbers of Some Graphs

TANG Jie-quan, SHU Jin-long   

  1. Department of Mathematics, East China Normal University, Shanghai 200062, China
  • Received:2005-01-17 Revised:2005-04-20 Online:2006-09-25 Published:2012-11-27

摘要： 运用图的最优填充分解定理和局部最优填充定理, 将一些特殊图类G1×G2, S(G)和双圈图分解为一些可求得最小填充数的图, 得到如下结果: (1)F(Pm×Pn)≦(m-2)(n-2), 其中m≧2, n≧2; (2)若G是有m条边的n阶2-连通图,则F(S(G))=m+F(G); (3) 设图G为双圈图,两个诱导圈的圈长分别为p和q, t为这两个圈公共部分的路上的顶点个数(不包括两个端点),则F(G)=p+q-t-6.

关键词: 填充数, 分解约化, 弦图, 双圈图 ,  ,

Abstract: By using the decomposition theorem and the local reductive elimination for the fill-in of graphs, the fill-in numbers of some special graphs, such as G1×G2, S(G) and double cyclic graphs were studied. And the following results were obtained: (1)F(Pm×Pn)≦(m-2)(n-2), where m≧2, n≧2; ; (2) if G is a 2-connected graph with m edges and n vertices, then F(S(G))=m+F(G); (3) let G be a double cyclic graph, the length of the two cycles being p and q, respectively, and t the number of the vertices which are both in the two cycles (the end points are excluded), then F(G)=p+q-t-6.

Key words: fill-in, chordal, decomposition theorem, double cyclic graphs  ,

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