4 papers · 1 filter
Spanning weakly even trees of graphs
Jiangdong Ai, M. N. Ellingham, Zhipeng Gao +5
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 o…
A short note on spanning even trees
Jiangdong Ai, Zhipeng Gao, Xiangzhou Liu +1
We call a tree is \emph{even} if every pair of its leaves is joined by a path of even length. Jackson and Yoshimoto~[J. Graph Theory, 2024] conjectured that every -regular n…
A variable version of the quasi-kernel conjecture
Jiangdong Ai, Xiangzhou Liu, Fei Peng
A quasi-kernel of a digraph is an independent set such that every vertex can reach in at most two steps. A 48-year conjecture made by P.L. Erdős and Székely, denoted th…
Piercing independent sets in graphs without large induced matching
Jiangdong Ai, Hong Liu, Zixiang Xu +1
Given a graph , denote by the smallest size of a subset of which intersects every maximum independent set of . We prove that any graph without induced match…