The Hamiltonian index of a graph and its branch-bonds


Xiong, L. and Broersma, H.J. and Li, X. (2001) The Hamiltonian index of a graph and its branch-bonds. [Report]

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Abstract:Let $G$ be an undirected and loopless finite graph that is not a path. The minimum $m$ such that the iterated line graph $L^m(G)$ 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 $h(G)\geq 2$ is given here. With it we will establish a sharp lower bound and a sharp upper bound for $h(G)$, respectively, which improves some known results of P.A. Catlin et al. [J. Graph Theory 14 (1990)] and H.-J. Lai [Discrete Mathematics 69 (1988)]. Examples show that $h(G)$ may reach all integers between the lower bound and the upper bound.
Item Type:Report
Electrical Engineering, Mathematics and Computer Science (EEMCS)
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Metis ID: 203117