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| On k-ordered Graphs Involved Degree Sum | |
| 作者姓名： | Zhi-quan Hu Feng TianDepartment of Mathematics Central China Normal University Wuhan 430079 ChinaInstitute of System Sciences Academy of Mathematics and System Sciences Chinese Academy of Sciences Beijing 100080 China |
| 作者单位： | Zhi-quan Hu，Feng TianDepartment of Mathematics，Central China Normal University，Wuhan 430079，ChinaInstitute of System Sciences，Academy of Mathematics and System Sciences，Chinese Academy of Sciences，Beijing 100080，China |
| 基金项目： | Partially supported by the National Natural Sciences Foundation of China (No.19831080). |
| 摘 要： | Abstract A graph G is k-ordered Hamiltonian,2≤k≤n,if for every ordered sequence S of k distinctvertlces of G,there exists a Hamiltonian cycle that encounters S in the given order. In this article, we provethat if G is a graph on n vertices with degree sum of nonadjacent vertices at least n+3k-9/2,then G is k-orderedHamiltonian for k=3,4,…,[n/19].We also show that the degree sum bound can be reduced to n+2[k/2]-2 ifk(G)≥3k-1/2 or δ(G)≥5k-4.Several known results are generalized. |
| 关 键 词： | κ-ordered fc-ordered Hamiltonian degree sum |
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