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arXiv · 2409.15522

Spanning weakly even trees of graphs

Jiangdong Ai·M. N. Ellingham·Zhipeng Gao·Yixuan Huang·Xiangzhou Liu·Songling Shan·Simon Špacapan·Jun Yue
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Abstract

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.

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Jiangdong Ai, M. N. Ellingham, Zhipeng Gao, Yixuan Huang, Xiangzhou Liu, Songling Shan, Simon Špacapan, Jun Yue. 2024-10-17. Spanning weakly even trees of graphs. https://arxiv.org/abs/2409.15522

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