Closure, stability and iterated line graphs with a 2-factor |
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Authors: | Akira Saito |
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Institution: | a Department of Computer Science, Nihon University, Sakurajosui 3-25-40, Setagaya-Ku, Tokyo 156-8550, Japan b Department of Mathematics, Beijing Institute of Technology, Beijing 100081, PR China c Department of Mathematics, Jiangxi Normal University, Nanchang 330022, PR China |
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Abstract: | We consider 2-factors with a bounded number of components in the n-times iterated line graph Ln(G). We first give a characterization of graph G such that Ln(G) has a 2-factor containing at most k components, based on the existence of a certain type of subgraph in G. This generalizes the main result of L. Xiong, Z. Liu, Hamiltonian iterated line graphs, Discrete Math. 256 (2002) 407-422]. We use this result to show that the minimum number of components of 2-factors in the iterated line graphs Ln(G) is stable under the closure operation on a claw-free graph G. This extends results in Z. Ryjá?ek, On a closure concept in claw-free graphs, J. Combin. Theory Ser. B 70 (1997) 217-224; Z. Ryjá?ek, A. Saito, R.H. Schelp, Closure, 2-factors and cycle coverings in claw-free graphs, J. Graph Theory 32 (1999) 109-117; L. Xiong, Z. Ryjá?ek, H.J. Broersma, On stability of the hamiltonian index under contractions and closures, J. Graph Theory 49 (2005) 104-115]. |
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Keywords: | 2-factor Iterated line graph Closure operation Claw-free graph |
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