On stability of the Hamiltonian index under contractions and closures

L. Xiong, Z. Ryjáček, Haitze J. Broersma

Research output: Book/ReportReportOther research output

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Abstract

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 $G$.
Original languageUndefined
Place of PublicationEnschede
PublisherUniversity of Twente, Department of Applied Mathematics
Publication statusPublished - 2002

Publication series

NameMemorandum
PublisherDepartment of Applied Mathematics, University of Twente
No.1622
ISSN (Print)0169-2690

Keywords

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

Cite this

Xiong, L., Ryjáček, Z., & Broersma, H. J. (2002). On stability of the Hamiltonian index under contractions and closures. (Memorandum; No. 1622). Enschede: University of Twente, Department of Applied Mathematics.
Xiong, L. ; Ryjáček, Z. ; Broersma, Haitze J. / On stability of the Hamiltonian index under contractions and closures. Enschede : University of Twente, Department of Applied Mathematics, 2002. (Memorandum; 1622).
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Xiong, L, Ryjáček, Z & Broersma, HJ 2002, 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.

Enschede : University of Twente, Department of Applied Mathematics, 2002. (Memorandum; No. 1622).

Research output: Book/ReportReportOther 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 $G$.

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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

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Xiong L, Ryjáček Z, Broersma HJ. On stability of the Hamiltonian index under contractions and closures. Enschede: University of Twente, Department of Applied Mathematics, 2002. (Memorandum; 1622).