### Abstract

Original language | Undefined |
---|---|

Place of Publication | Enschede |

Publisher | University of Twente, Department of Applied Mathematics |

Publication status | Published - 2002 |

### Publication series

Name | Memorandum |
---|---|

Publisher | Department of Applied Mathematics, University of Twente |

No. | 1622 |

ISSN (Print) | 0169-2690 |

### Keywords

- MSC-05C45
- IR-65809
- EWI-3442
- MSC-05C35

### Cite this

*On stability of the Hamiltonian index under contractions and closures*. (Memorandum; No. 1622). Enschede: University of Twente, Department of Applied Mathematics.

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*On stability of the Hamiltonian index under contractions and closures*. Memorandum, no. 1622, University of Twente, Department of Applied Mathematics, Enschede.

**On stability of the Hamiltonian index under contractions and closures.** / Xiong, L.; Ryjáček, Z.; Broersma, Haitze J.

Research output: Book/Report › Report › Other research output

TY - BOOK

T1 - On stability of the Hamiltonian index under contractions and closures

AU - Xiong, L.

AU - Ryjáček, Z.

AU - Broersma, Haitze J.

PY - 2002

Y1 - 2002

N2 - The hamiltonian index of a graph $G$ is the smallest integer $k$ such that the $k$-th iterated line graph of $G$ is hamiltonian. We first show that, with one exceptional case, adding an edge to a graph cannot increase its hamiltonian index. We use this result to prove that neither the contraction of an $A_G(F)$-contractible subgraph $F$ of a graph $G$ nor the closure operation performed on $G$ (if $G$ is claw-free) affects the value of the hamiltonian index of a graph $G$.

AB - The hamiltonian index of a graph $G$ is the smallest integer $k$ such that the $k$-th iterated line graph of $G$ is hamiltonian. We first show that, with one exceptional case, adding an edge to a graph cannot increase its hamiltonian index. We use this result to prove that neither the contraction of an $A_G(F)$-contractible subgraph $F$ of a graph $G$ nor the closure operation performed on $G$ (if $G$ is claw-free) affects the value of the hamiltonian index of a graph $G$.

KW - MSC-05C45

KW - IR-65809

KW - EWI-3442

KW - MSC-05C35

M3 - Report

T3 - Memorandum

BT - On stability of the Hamiltonian index under contractions and closures

PB - University of Twente, Department of Applied Mathematics

CY - Enschede

ER -