| Hamilton有向图的一个新的充分条件 |
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| 引用本文： | 王世英,原军,刘爱霞. Hamilton有向图的一个新的充分条件[J]. 山西大学学报(自然科学版), 2007, 30(2): 143-148 |
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| 作者姓名： | 王世英 原军 刘爱霞 |
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| 作者单位： | 山西大学,数学科学学院,山西,太原,030006 |
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| 摘 要： | 设D是n(≥2)阶强连通有向图.猜想:如果D中每一对不相邻且有公共外邻或公共内邻的顶点x,y都有d(x) d(y)≥2n-1,那么D是Hamilton有向图.文章证明了当n≥7时,若D中每一个不相邻且有公共外邻或公共内邻的顶点x,y都有d(x) d(y)≥(5n)/2-5,则D是Hamilton有向图.当3≤n≤6时,存在非Hamilton有向图D满足D中每一对不相邻且有公共外邻或公共内邻的顶点x,y都有d(x) d(y)≥(5n)/2-5.
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| 关 键 词： | 有向图 Hamilton图 Hamilton有向图 |
| 文章编号： | 0253-2395（2007）02-0143-06 |
| 修稿时间： | 2007-01-09 |
A New Sufficient Condition for Hamiltonian Digraphs |
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| WANG Shi-ying,YUAN Jun,LIU Ai-xia. A New Sufficient Condition for Hamiltonian Digraphs[J]. Journal of Shanxi University (Natural Science Edit, 2007, 30(2): 143-148 |
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| Authors: | WANG Shi-ying YUAN Jun LIU Ai-xia |
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| Affiliation: | School of Mathematical Sciences ,Shanxi University ,Taiyuan 030006 ,China |
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| Abstract: | Let D be a strongly connected digraph of order n≥2. It has been conjectured that if d(x)+d(y)≥2n-1 for every pair of non-adjacent vertices x,y with a common out-neighbor or a common in-neighbor. then D is hamiltonian. In this paper.it is proved that for a digraph D of order n≥7,if d(x)+d(y)≥5n/2-5 for every pair of non-adjacent vertices x,y with a common out-neighbor or a common in-neighbor,then D is hamiltonian and for 3≤ n≤6,there are non-hamiltonian digraphs satisfying that d(x) +d(y)≥5n/2-5 for every pair of non-adjacent vertices x,y with a common out-neighbor or a common in-neighbor. |
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| Keywords: | digraphs hamiltonian cycles hamiltonian digraphs |
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