Spanning weakly even trees of graphs
| Autor: | Ai, Jiangdong, Ellingham, M. N., Gao, Zhipeng, Huang, Yixuan, Liu, Xiangzhou, Shan, Songling, Špacapan, Simon, Yue, Jun |
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| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | Let $G$ be a graph (with multiple edges allowed) and let $T$ be a tree in $G$. We say that $T$ is $\textit{even}$ if every leaf of $T$ belongs to the same part of the bipartition of $T$, and that $T$ is $\textit{weakly even}$ if every leaf of $T$ that has maximum degree in $G$ belongs to the same part of the bipartition of $T$. We confirm two recent conjectures of Jackson and Yoshimoto by showing that every connected graph that is not a regular bipartite graph has a spanning weakly even tree. Comment: 6 pages. This article represents a merger of arXiv:2409.15522v1 and arxiv:2408.07056 |
| Databáze: | arXiv |
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