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2024 Spanning Trees with at most $5$ Leaves and Branch Vertices in Total of $K_{1,5}$-free Graphs
Pham Hoang Ha, Nguyen Hoang Trang
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Taiwanese J. Math. Advance Publication 1-9 (2024). DOI: 10.11650/tjm/240606

Abstract

In this paper, we prove that every $n$-vertex connected $K_{1,5}$-free graph $G$ with $\sigma_{4}(G) \geq n-1$ contains a spanning tree with at most $5$ leaves and branch vertices in total. Moreover, the degree sum condition “$\sigma_{4}(G) \geq n-1$” is best possible.

Acknowledgments

We would like to thank the referees for their valuable comments which help us improve this research.

Citation

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Pham Hoang Ha. Nguyen Hoang Trang. "Spanning Trees with at most $5$ Leaves and Branch Vertices in Total of $K_{1,5}$-free Graphs." Taiwanese J. Math. Advance Publication 1 - 9, 2024. https://doi.org/10.11650/tjm/240606

Information

Published: 2024
First available in Project Euclid: 30 June 2024

Digital Object Identifier: 10.11650/tjm/240606

Subjects:
Primary: 05C05 , 05C07 , 05C69

Keywords: $K_{1,5}$-free , degree sum , spanning tree

Rights: Copyright © 2024 The Mathematical Society of the Republic of China

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