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| 点度与图的上可嵌入性 | |
| 引用本文： | 张启明,黄元秋,任俊峰.点度与图的上可嵌入性[J].应用数学学报,2009,32(5). |
| 作者姓名： | 张启明 黄元秋 任俊峰 |
| 作者单位： | 1. 中南大学数学科学与计算技术学院,长沙,410075;湖南工业大学理学院,株洲期,412007 2. 湖南师范大学数学系,长沙,410081 3. 河南理工大学数学与信息科学学院,焦作,454000 |
| 基金项目： | 国家自然科学基金资助项目，教育部新世纪优秀人才支持项目 |
| 摘 要： | 本文证明了:(1) 设G是2-连通简单图,且不含K_3,若对任意一对距离为2的点u,u,有max{d(u),d(u)}>n/3-1,其中n=|V(G)|,则G是上可嵌入的,且条件中不等式的界"n/3-1"是不可达的;(2) 设G是3-连通简单图,若对任意依次相邻的三点u,u,W,有max{d(u),d(u),d(w)}≥n/6+1,其中n=|V(G)|,则G是上可嵌入的,且条件中不等式的界"n/6+1"是最好的. |
| 关 键 词： | 图 Betti亏数 上可嵌入性 点度 |
The Vertice Degree Condition on Upper Embeddability of Graphs |
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| ZHANG QIMING,HUANG YUANQIU,REN JUNFENG.The Vertice Degree Condition on Upper Embeddability of Graphs[J].Acta Mathematicae Applicatae Sinica,2009,32(5). | |
| Authors: | ZHANG QIMING HUANG YUANQIU REN JUNFENG |
| Abstract: | This paper mainly prove:(1) Let G is a 2-vertice connected simple graph which doesn't have complete sub-graph K_3. For any two vertices u, v of V(G) whose distance is 2 between them, it satisfies max {d(u), d(v)} >n/3-1, then G is upper embeddable, furthermore, the lower bound does impossibly arrive;(2) Let G is a 3-vertice connected simple graph for any three adjacent vertices u, v and w of V(G), i.e., uv ∈ E(G) and vw ∈ E(G), it satisfies max{d(u), d(v), d(w)}≥n/6+1,then G is upper embeddable, furthermore, the lower bound is best possible. |
| Keywords: | graph Betti deficiency upper embeddability vertice degree |
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