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
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. 28 (5) 847 - 855, October, 2024. https://doi.org/10.11650/tjm/240606
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