Abstract
| Original language | Undefined |
|---|---|
| Place of Publication | Enschede |
| Publisher | University of Twente |
| Number of pages | 13 |
| Publication status | Published - 2001 |
Publication series
| Name | Memorandum Faculteit TW |
|---|---|
| Publisher | University of Twente |
| No. | 1611 |
| ISSN (Print) | 0169-2690 |
Keywords
- MSC-05C35
- EWI-3431
- MSC-05C45
- METIS-203117
- IR-65798
Cite this
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The Hamiltonian index of a graph and its branch-bonds. / Xiong, L.; Liming, X.; Broersma, Haitze J.; Li, X.; Li, Xueliang.
Enschede : University of Twente, 2001. 13 p. (Memorandum Faculteit TW; No. 1611).Research output: Book/Report › Report › Professional
TY - BOOK
T1 - The Hamiltonian index of a graph and its branch-bonds
AU - Xiong, L.
AU - Liming, X.
AU - Broersma, Haitze J.
AU - Li, X.
AU - Li, Xueliang
N1 - Imported from MEMORANDA
PY - 2001
Y1 - 2001
N2 - 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.
AB - 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.
KW - MSC-05C35
KW - EWI-3431
KW - MSC-05C45
KW - METIS-203117
KW - IR-65798
M3 - Report
T3 - Memorandum Faculteit TW
BT - The Hamiltonian index of a graph and its branch-bonds
PB - University of Twente
CY - Enschede
ER -