@article{2e3eff81d37c4e1b9129cf2ab645d972,
title = "The hamiltonian index of a graph and its branch-bonds",
abstract = "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.",
keywords = "Reduction method, Hamiltonian index, Branch-bond, Iterated line graph",
author = "Liming Xiong and H.J. Broersma and Xueliang Li and MingChu Li",
year = "2004",
doi = "10.1016/j.disc.2004.01.018",
language = "English",
volume = "285",
pages = "279--288",
journal = "Discrete mathematics",
issn = "0012-365X",
publisher = "Elsevier",
number = "1-3",
}