强浸入关系下不含长交替路径的有向图的良拟序

交错群与对称群的顶点本原 s-弧传递有向图中 s 的界

Bounding $s$ for vertex-primitive $s$-arc-transitive digraphs of alternating and symmetric groups

本文针对 Praeger 提出的有限顶点本原 s-弧传递有向图的上界问题，在群为交错群或对称群的情形下证明了 s ≤ 2。

关于无洋葱星浸入的有向图

On digraphs without onion star immersions

本研究刻画了排除固定洋葱星浸入的有向图结构，证明了无向对偶命题的两个有向版本，为有向图浸入理论提供了新的结构结果。

欧拉图的良quis序：受限刻痕宽度

Well-Quasi-Ordering Eulerian Digraphs: Bounded Carving Width

本文证明了具有受限刻痕宽度的欧拉图类在强浸入下是良quis序的，并提出了一种新的强浸入概念。同时指出无界度数的欧拉图类在强浸入下不满足良quis序，但弱浸入下可能满足。

Vertex-primitive s-arc-transitive digraphs of alternating and symmetric groups

A fascinating problem on digraphs is the existence problem of the finiteupper bound on s for all vertex-primitive s-arc-transitive digraphs except directed cycles (which is known to be reduced to the almost simple groups case). In this paper,we prove that s 2 for all G-vertex-primitive s-arc-transitive digraphs with G an (insoluble) alternating or symmetric group, which makes an important progress towards a solution of the problem. The proofs involves some methods that may be used to investigate other almost simple groups cases.

Directed Hamilton cycles in digraphs and matching alternating Hamilton cycles in bipartite graphs

In 1972, Woodall raised the following Ore type condition for directed Hamilton cycles in digraphs: Let $D$ be a digraph. If for every vertex pair $u$ and $v$, where there is no arc from $u$ to $v$, we have $d^+u)+d^-(v)\geq |D|$, then $D$ has a directed Hamilton cycle. By a correspondence between bipartite graphs and digraphs, the above result is equivalent to the following result of Las Vergnas: Let $G = (B,W)$ be a balanced bipartite graph. If for any $b \in B$ and $w \in W$, where $b$ and $w$ are nonadjacent, we have $d(w)+d(b) \geq |G|/2 + 1$, then every perfect matching of $G$ is containe…

有向图的构型空间与独立复形的拓扑持续性

Topological persistence of configuration spaces and independence complexes for digraphs

该研究探讨有向图及基础图的（路径）构型空间与独立复形的拓扑持续性，构建相关典范嵌入，将路径同调应用于路径独立复形，得到了关于Shannon容量的相关结论。

锦标赛中有向图的浸入

Immersions of directed graphs in tournaments

本文研究锦标赛中有向图的浸入问题，证明了任意具有O(k)个顶点的锦标赛必含k个顶点的传递锦标赛的1-浸入，并进一步证明最小出度至少为Ck的锦标赛必含k个顶点的完全有向图的2-浸入，且这些界在相应意义下都是紧的。

交替定向n边阶梯有向图的邻接谱

On the Adjacency spectra of alternating-oriented $n$-gonal staircase digraphs

研究了交替定向n边阶梯有向图的邻接谱，通过分析其邻接矩阵的结构和性质，确定了非零特征值的分布和重数，并与Padovan螺旋数相关联。

2-边着色多重图中的交替哈密顿圈

Alternating Hamiltonian cycles in $2$-edge-colored multigraphs

本文研究2-边着色多重图中的交替哈密顿圈，通过施加局部闭性条件，给出了2-M-闭多重图存在交替哈密顿圈的充要条件，并构造了反例族。