| 收缩临界6连通图中的6度顶点 |
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| 引用本文： | 赵巧凤,覃城阜,袁旭东,李敏.收缩临界6连通图中的6度顶点[J].广西师范大学学报(自然科学版),2005,23(2):38-43. |
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| 作者姓名： | 赵巧凤 覃城阜 袁旭东 李敏 |
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| 作者单位： | 广西师范大学数学与计算机科学学院,广西,桂林,541004;广西师范大学数学与计算机科学学院,广西,桂林,541004;广西师范大学数学与计算机科学学院,广西,桂林,541004;广西师范大学数学与计算机科学学院,广西,桂林,541004 |
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| 基金项目： | NSFC of China (10171022);Guangxi Youth Science Foundation (0135028) |
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| 摘 要： | 如果6连通图的一条边收缩后使得所得到的图仍是6连通,则这条边称为6可收缩边.一个不包含6可收缩边的非完全图被称为收缩临界6连通图.由Egawa的结果可知收缩临界6连通图中有6度点.设G是收缩临界6连通图,用V6表示G中6度点的集合.Ando等人通过证明存在常数c使得|V6|＞c|V(G)|且c≥(1)/(7).现将这一常数改进为c≥(1)/(5).
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| 关 键 词： | 6连通 6可收缩边 断片 度 |
| 文章编号： | 1001-6600(2005)02-0038-06 |
VERTICES OF DEGREE 6 IN A CONTRACTION-CRITICAL 6 CONNECTED GRAPH |
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| ZHAO Qiao-feng,QIN Cheng-fu,YUAN Xu-dong,LI Min.VERTICES OF DEGREE 6 IN A CONTRACTION-CRITICAL 6 CONNECTED GRAPH[J].Journal of Guangxi Normal University(Natural Science Edition),2005,23(2):38-43. |
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| Authors: | ZHAO Qiao-feng QIN Cheng-fu YUAN Xu-dong LI Min |
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| Abstract: | An edge of a 6 connected graph is said to be 6-contractible if its contraction results still in a 6 connected graph.A noncomplete 6 connected graph is called contraction-critical if it has no any 6-contractible edge.Let G be a contraction-critical 6 connected graph.By Egawa's result,G has a vertex of degree 6.Let V6 denote the set of vertices of degree 6 in G.Recently,Ando et.al showed that there is a constant c such that |V6|≥c|V(G)|,and c≥1/7.In this note,it is proved that c≥1/5. |
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| Keywords: | 6 connected 6-contractible edge fragment degree |
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