On stability of the Hamiltonian index under contractions and closures

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

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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.