The hamiltonian index of a graph and its branch-bonds

Liming Xiong, H.J. Broersma, Xueliang Li, MingChu Li

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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.
Original languageEnglish
Pages (from-to)279-288
Number of pages9
JournalDiscrete mathematics
Issue number1-3
Publication statusPublished - 2004


  • Reduction method
  • Hamiltonian index
  • Branch-bond
  • Iterated line graph

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