@book{d8f529b742334c4c89c45fdaa852ae6b,

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 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.",

keywords = "MSC-05C35, EWI-3431, MSC-05C45, METIS-203117, IR-65798",

author = "L. Xiong and X. Liming and Broersma, {Haitze J.} and X. Li and Xueliang Li",

note = "Imported from MEMORANDA",

year = "2001",

language = "Undefined",

series = "Memorandum Faculteit TW",

publisher = "University of Twente",

number = "1611",

address = "Netherlands",

}