5 papers · 1 filter
Quasi-kernels in Hereditary Classes and Applications to Break
Jiangdong Ai, Tianyu Huang, Xiangzhou Liu +2
Recently, Nguyen, Seymour and Scott verified the small quasi-kernel conjecture for split digraphs, and initiated the study of quasi-kernels in break digraphs. Following their resea…
Feedback vertex sets of digraphs with bounded maximum degree
Jiangdong Ai, Gregory Gutin, Xiangzhou Liu +2
A digraph is an oriented graph if does not have a pair of opposite arcs. The degree of a vertex of is the sum of the in-degree and out-degree of Let b…
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…