Abstract
We consider even factors with a bounded number of components in the n-times iterated line graphs L n(G). We present a characterization of a simple graph G such that L n(G) has an even factor with at most k components, based on the existence of a certain type of subgraphs in G. Moreover, we use this result to give some upper bounds for the minimum number of components of even factors in L n(G) and also show that the minimum number of components of even factors in L n(G) is stable under the closure operation on a claw-free graph G, which extends some known results. Our results show that it seems to be NP-hard to determine the minimum number of components of even factors of iterated line graphs. We also propose some problems for further research.
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Acknowledgements
This work was supported by National Natural Science Foundation of China (Grant Nos. 11471037 and 11171129) and Specialized Research Fund for the Doctoral Program of Higher Education (Grant No. 20131101110048).
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Lv, S., Xiong, L. Even factors with a bounded number of components in iterated line graphs. Sci. China Math. 60, 177–188 (2017). https://doi.org/10.1007/s11425-015-0506-3
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DOI: https://doi.org/10.1007/s11425-015-0506-3