论文标题
第二个邻域猜想缺少$ \ {c_ {4}，\ edline {c_ {4}}，s_ {3}，$ seaker and co-creair $ \} $ - 免费图
The Second Neighborhood Conjecture for Oriented Graphs Missing $\{C_{4}, \overline{C_{4}}, S_{3},$ chair and co-chair$\}$-Free Graph
论文作者
论文摘要
西摩的第二个社区猜想（SNC）断言，每个面向的图形都有一个顶点，其第一个邻居最多的最大程度与其第二个邻居一样大。在本文中，我们证明，如果$ g $是包含$ c_4 $，$ \ overline {c_4} $，$ s_3 $，椅子和$ \ overline {cair {cair} $的图表，那么缺少$ g $的每一个方向的$ g $都可以满足这个猜想。结果，我们推断出猜想为每个方向的图所保留，缺少阈值图，广义梳子或星星。
Seymour's Second Neighborhood Conjecture (SNC) asserts that every oriented graph has a vertex whose first out-neighborhood is at most as large as its second out-neighborhood. In this paper, we prove that if $G$ is a graph containing no induced $C_4$, $\overline{C_4}$, $S_3$, chair and $\overline{chair}$, then every oriented graph missing $G$ satisfies this conjecture. As a consequence, we deduce that the conjecture holds for every oriented graph missing a threshold graph, a generalized comb or a star.
