Spanning trees of claw-free graphs with few leaves and branch vertices
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866909923314499584 |
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| author | Ha, Pham Hoang Hien, Nguyen Gia |
| author_facet | Ha, Pham Hoang Hien, Nguyen Gia |
| contents | Let $T$ be a tree. A vertex of degree one is a \emph{leaf} of $T$ and a vertex of degree at least three is a \emph{branch vertex} of $T$. A graph is said to be claw-free if it does not contain $K_{1,3}$ as an induced subgraph. In this paper, we study the spanning trees with a bounded number of leaves and branch vertices of claw-free graphs. Applying the main results, we also give some improvements of previous results on the spanning trees with few branch vertices for the case of claw-free graphs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_07339 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Spanning trees of claw-free graphs with few leaves and branch vertices Ha, Pham Hoang Hien, Nguyen Gia Combinatorics Let $T$ be a tree. A vertex of degree one is a \emph{leaf} of $T$ and a vertex of degree at least three is a \emph{branch vertex} of $T$. A graph is said to be claw-free if it does not contain $K_{1,3}$ as an induced subgraph. In this paper, we study the spanning trees with a bounded number of leaves and branch vertices of claw-free graphs. Applying the main results, we also give some improvements of previous results on the spanning trees with few branch vertices for the case of claw-free graphs. |
| title | Spanning trees of claw-free graphs with few leaves and branch vertices |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2502.07339 |