| Autor: |
Yan, Zilong, Peng, Yuejian |
| Rok vydání: |
2021 |
| Předmět: |
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| Druh dokumentu: |
Working Paper |
| Popis: |
We say that a graph $F$ can be embedded into a graph $G$ if $G$ contains an isomorphic copy of $F$ as a subgraph. Guo and Volkmann \cite{GV} conjectured that if $G$ is a connected graph with at least $n$ vertices and minimum degree at least $n-3$, then any tree with $n$ vertices and maximum degree at most $n-4$ can be embedded into $G$. In this paper, we give a result slightly stronger than this conjecture and obtain a sufficient and necessary condition that a tree with $n$ vertices and maximum degree at most $n-3$ can be embedded into a connected graph G with at least $n$ vertices and minimum degree at least $n-3$. Our result implies that the conjecture of Guo and Volkmann is true with one exception. We also give an application to the Ramsey number of a tree versus a star. |
| Databáze: |
arXiv |
| Externí odkaz: |
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