A generalisation of Seymour's second neighbourhood conjecture

Seymour紧导向

Seymour-tight orientations

研究Seymour第二邻域猜想的几乎反例，探讨Seymour紧导向的性质及其在勒克西克图形积中的封闭性，并构造反例。

Seymour's second neighbourhood conjecture for quasi-transitive oriented graphs

Seymour's second neighbourhood conjecture asserts that every oriented graph has a vertex whose second out-neighbourhood is at least as large as its out-neighbourhood. In this paper, we prove that the conjecture holds for quasi-transitive oriented graphs, which is a superclass of tournaments and transitive acyclic digraphs. A digraph $D$ is called quasi-transitive is for every pair $xy,yz$ of arcs between distinct vertices $x,y,z$, $xz$ or $zx$ ("or" is inclusive here) is in $D$.

Seymour 第二邻域猜想：随机图与归约

Seymour's second neighbourhood conjecture: random graphs and reductions

本文研究 Seymour 第二邻域猜想，证明在随机图 G(n,p) 中当 p<1/2 时猜想几乎必然成立，并通过 p=1/2 的障碍及最小度分析给出该猜想的两个归约。

关于西摩和沙利文的第二邻域猜想

On Seymour's and Sullivan's Second Neighbourhood Conjectures

研究西摩和沙利文关于有向图顶点邻域关系的第二邻域猜想，给出满足沙利文猜想的传递三角形数量充分条件，证明其对平面图等成立，还表明对一些定向分裂图族两个猜想也成立。