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On stability of the Hamiltonian index under contractions and closures

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Xiong, L. and Ryjáček, Z. and Broersma, H.J. (2002) On stability of the Hamiltonian index under contractions and closures. [Report]

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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 $G$.
Item Type:Report
Faculty:
Electrical Engineering, Mathematics and Computer Science (EEMCS)
Research Group:
Link to this item:http://purl.utwente.nl/publications/65809
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