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arXiv · 2412.16505

Spectral conditions for spanning $k$-trees or $k$-ended-trees of $t$-connected graphs

Jifu Lin·Zenan Du·Xinghui Zhao·Lihua You
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Abstract

Let $G$ be a connected graph of order $n$. A spanning $k$-tree of $G$ is a spanning tree with the maximum degree at most $k$, and a spanning $k$-ended-tree of $G$ is a spanning tree at most $k$ leaves, where $k\geq2$ is an integer. This paper establishes some spectral conditions for the existence of spanning $k$-trees or spanning $k$-ended-trees in $t$-connected graphs, which generalize the results of Fan et al. (2022) and Zhou (2010), and improve the results of Fiedler et al. (2010), Ao et al. (2023) and Ao et al. (2025).

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Jifu Lin, Zenan Du, Xinghui Zhao, Lihua You. 2024-12-21. Spectral conditions for spanning $k$-trees or $k$-ended-trees of $t$-connected graphs. https://arxiv.org/abs/2412.16505

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