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On stability of the hamiltonian index under contractions and closures

✍ Scribed by Liming Xiong; Zdeněk Ryjáček; Hajo Broersma

Publisher
John Wiley and Sons
Year
2005
Tongue
English
Weight
113 KB
Volume
49
Category
Article
ISSN
0364-9024

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✦ Synopsis

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. AMS Subject Classification (2000): 05C45, 05C35. © 2005 Wiley Periodicals, Inc. J Graph Theory

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