| 距离无爪图的Hamilton性 |
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| 引用本文： | 王兵. 距离无爪图的Hamilton性[J]. 安徽大学学报(自然科学版), 2004, 28(1): 20-23,29 |
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| 作者姓名： | 王兵 |
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| 作者单位： | 枣庄师范专科学校,数学系,山东,枣庄,277160 |
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| 摘 要： | 距离无爪图类属于无爪图类。所谓距离无爪图是对图中的每一个顶点,其距离为的邻域的独立数均不超过3的图.F.BruceShephed已证明:若G是距离无爪图且G是2─连通的,则G有Hamilton路;若G是距离无爪图且G是3─连通的,则G有Hamilton圈.本文在此基础上,定义了一种新的禁用子图──网全爪,首先证明了2-连通的、无网的距离无爪图有Hamilton圈.又证明了2-连通的有网、无网全爪的距离无爪图有Hamilton圈.
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| 关 键 词： | 无网图 距离无爪图 网全爪 |
| 文章编号： | 1000-2162(2004)01-0020-04 |
The hamiltonian of distance claw-free graphs |
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| WANG Bing. The hamiltonian of distance claw-free graphs[J]. Journal of Anhui University(Natural Sciences), 2004, 28(1): 20-23,29 |
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| Authors: | WANG Bing |
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| Abstract: | Distance claw-free consists of those claw-free graphs such that for each vertex v, the set of vertices at distance i from v does not contain an independent subset of size three.F.Bruce shepherd has proved that: if G∈DC and G is 2-connected, then G has a Hamilton path,furthermore,if G∈DC and G is 3-connected then G has a Hamilton path.Basing on these results, the paper defines a new forbidden subgraph,which is net completed-claw. The paper proves the 2-connected、distance claw-free graph has hamilton cycle on the conditions of net-free or net complete claw -free. |
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| Keywords: | net-free graph distance claw-free graph net complete claw |
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