关于可迹迭代线图与Hamilton路指数
On traceable iterated line graph and hamiltonian path index
摘要：
Xiong和Liu [L. Xiong和Z. Liu，Hamiltonian iterated line graphs，Discrete Math.256（2002）407-422]给出了图$G$的特征，其中第$n$个迭代线图$L^n(G)$是哈密尔顿的，对于$n\ge2$。本文研究了$L^n(G)$中Hamilton路的存在性，给出了$G$中$L^n(G)$有Hamilton路的一个刻划，作为应用，我们给出了图的Hamilton路指数的几个上界.
英文摘要：
Xiong and Liu [L. Xiong and Z. Liu, Hamiltonian iterated line graphs, Discrete Math. 256 (2002) 407-422] gave a characterization of the graphs $G$ for which the $n$-th iterated line graph $L^n(G)$ is hamiltonian, for $n\ge2$. In this paper, we study the existence of a hamiltonian path in $L^n(G)$, and give a characterization of $G$ for which $L^n(G)$ has a hamiltonian path. As applications, we use this characterization to give several upper bounds on the hamiltonian path index of a graph.
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