本质集的邻域并和图的哈密尔顿性 |
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引用本文: | 徐新萍.本质集的邻域并和图的哈密尔顿性[J].东北数学,2004,20(1):41-50. |
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作者姓名: | 徐新萍 |
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作者单位: | SchoolofMathematicsandComputerScience,NanjingNormalUniversity,Nanjing,210097;DepartmentofMathematicsandComputerScience,JiangsuEducationCollege,Nanjing,210013 |
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摘 要: | Let G be a graph. An independent set Y in G is called an essential independent set (or essential set for simplicity) if there is {Y1, Y2} 包含于Y such that dist (y1,y2)=2. In this paper, we use the technique of the vertex insertion on l-connected (l=k or k 1, k≥2) graphs to provide a unified proof for G to be hamiltonian, or hamiltonian-connected. The sufficient conditions are expressed an inequality on ∑i=1 K|N(Yi)| b|N(y0)| and n(Y) for each essential set Y={y0,y1,…,yk}, where b (1≤b≤k)is an integer,Yi={yi,yi-1,…,yi-(b-1}包含于Y\{y0} for i属于V(G):dist(v,Y)≤2}|.
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关 键 词: | 本质集 邻域并和图 哈密尔顿圈 连通图 |
The Neighborhood Union of Essential Sets and Hamiltonicity of Graphs |
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