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Spectral radius and k-factor-critical graphs

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Abstract

For a nonnegative integer k, a graph G is said to be k-factor-critical if \(G-Q\) admits a perfect matching for any \(Q\subseteq V(G)\) with \(|Q|=k\). In this article, we prove spectral radius conditions for the existence of k-factor-critical graphs. Our result generalizes one previous result on perfect matchings of graphs. Furthermore, we claim that the bounds on spectral radius in Theorem 3.1 are sharp.

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Acknowledgements

The authors are grateful to the anonymous referees for their valuable comments, suggestions, and corrections which improve the presentation of the original manuscript. This work was supported by the Natural Science Foundation of Jiangsu Province (Grant No. BK20241949). Project ZR2023MA078 supported by Shandong Provincial Natural Science Foundation.

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Authors and Affiliations

  1. School of Science, Jiangsu University of Science and Technology, Zhenjiang, 212100, Jiangsu, China

    Sizhong Zhou

  2. School of Mathematical Sciences, Nanjing Normal University, Nanjing, 210023, Jiangsu, China

    Zhiren Sun

  3. School of Science, Dalian Jiaotong University, Dalian, 116028, Liaoning, China

    Yuli Zhang

Authors
  1. Sizhong Zhou
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  2. Zhiren Sun
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  3. Yuli Zhang
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Correspondence to Yuli Zhang.

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Zhou, S., Sun, Z. & Zhang, Y. Spectral radius and k-factor-critical graphs. J Supercomput 81, 456 (2025). https://doi.org/10.1007/s11227-024-06902-3

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  • DOI: https://doi.org/10.1007/s11227-024-06902-3

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