Abstract
A tree T is called a k-tree if the maximum degree of T is at most k. In this paper, we give a sufficient condition for a graph to have a k-tree containing specified vertices as following: let G be a connected graph and let S be a subset of V(G). If \(\alpha _G(S)\le (k-1)\kappa _G(S)+1\), then G has a k-tree containing S. Moreover, this condition is sharp.
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Acknowledgements
The author would like to thank Professor Mikio Kano for his valuable comments. The author is graceful to the referees for careful reading and useful comments.
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This work was in part supported by the NSFC (11601041), Open Research Fund Program of Institute of Applied Mathematics Yangtze University (KF1601), The Yangtze Youth Fund (70107021).
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Yan, Z. Independence Number and k-Trees of Graphs. Graphs and Combinatorics 33, 1089–1093 (2017). https://doi.org/10.1007/s00373-017-1821-4
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DOI: https://doi.org/10.1007/s00373-017-1821-4