Spanning weakly even trees of graphs
Jiangdong Ai, M. N. Ellingham, Zhipeng Gao, Yixuan Huang, Xiangzhou, Liu, Songling Shan, Simon \v{S}pacapan, Jun Yue

TL;DR
This paper proves that every connected non-regular bipartite graph contains a spanning weakly even tree, confirming two recent conjectures in graph theory.
Contribution
It establishes the existence of spanning weakly even trees in a broad class of graphs, resolving two conjectures by Jackson and Yoshimoto.
Findings
Every connected non-regular bipartite graph has a spanning weakly even tree.
The result confirms two recent conjectures in graph theory.
The paper advances understanding of bipartite graph structures.
Abstract
Let be a graph (with multiple edges allowed) and let be a tree in . We say that is if every leaf of belongs to the same part of the bipartition of , and that is if every leaf of that has maximum degree in belongs to the same part of the bipartition of . 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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Taxonomy
TopicsAdvanced Graph Theory Research · Complexity and Algorithms in Graphs · Graph Labeling and Dimension Problems
