2024/09/23 by Ai, Jiangdong, Ellingham, M. N., Gao, Zhipeng +5
#05C05 (Primary) 05C07 (Secondary) #Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.2409.15522
Let G be a graph (with multiple edges allowed) and let T be a tree in G. We say that T is even if every leaf of T belongs to the same part of the bipartition of T, and that T is 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.