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The Spectral Radius and \({\mathcal {P}}_{\ge \ell }\)-Factors of Graphs Involving Minimum Degree

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Abstract

For an integer \(\ell \ge 2\), a \({\mathcal {P}}_{\ge \ell }\)-factor of a graph G is a spanning subgraph in which each component is a path of order at least \(\ell \). In this paper, we characterize the extremal graphs with maximum spectral radius among all connected graphs of given order with prescribed minimum degree and without a \({\mathcal {P}}_{\ge 2}\)-factor or a \({\mathcal {P}}_{\ge 3}\)-factor. This generalizes the result in Li and Miao (Discrete Math 344:112588, 2021).

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Acknowledgements

We would like to thank the anonymous referees for their helpful comments which improve the paper.

Funding

The author is supported by NSFC (No.12226304) and NSF of Shandong Province (No. ZR2022QA045).

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  1. School of Mathematics and Statistics, Shandong University of Technology, Zibo, 255049, Shandong, People’s Republic of China

    Wenqian Zhang

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  1. Wenqian Zhang
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Correspondence to Wenqian Zhang.

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Zhang, W. The Spectral Radius and \({\mathcal {P}}_{\ge \ell }\)-Factors of Graphs Involving Minimum Degree. Graphs and Combinatorics 38, 176 (2022). https://doi.org/10.1007/s00373-022-02584-x

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