The hamiltonian index of a graph and its branch-bonds
The hamiltonian index of a graph and its branch-bonds
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DOI：
10.1016/j.disc.2004.01.018
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发表时间：
2004-08
期刊：
影响因子：
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通讯作者：
Liming Xiong;H. Broersma;Xueliang Li;Mingchu Li
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文献类型：
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作者：
Liming Xiong;H. Broersma;Xueliang Li;Mingchu Li
设G是一个无向无环的有限非路图，使得迭代线图Lm（G）是Hamilton图的最小整数m称为G的Hamilton指数，记为h（G）.本文给出了确定图G的哈密尔顿指数的一种约化方法，其中h（G）≠ 2。我们利用它分别建立了h（G）的一个尖下界和一个尖上界，从而改进了Catlin等[J. Graph Theory 14（1990）347]和Hong-Jian Lai [Discrete Math.69（1988）43]的一些已知结果.实例表明，h（G）可以达到上界和下界之间的所有整数.我们还提出了一些问题。
Let G be an undirected and loopless finite graph that is not a path. The smallest integer m such that the iterated line graph Lm(G) is hamiltonian is called the hamiltonian index of G, denoted by h(G). A reduction method to determine the hamiltonian index of a graph G with h(G)⩾2 is given here. We use it to establish a sharp lower bound and a sharp upper bound on h(G), respectively, thereby improving some known results of Catlin et al. [J. Graph Theory 14 (1990) 347] and Hong-Jian Lai [Discrete Math. 69 (1988) 43]. Examples show that h(G) may reach all integers between the lower bound and the upper bound. We also propose some questions on the topic.