论文标题
在线图中存在闭合
Existential Closure in Line Graphs
论文作者
论文摘要
如果对于所有与$ | a \ cup b | = n $的不相交的顶点$ a $ a $ a $ a $ a $ a $ a \ a \ cup b | = n $的$ g $是{\ it $ n $ - 已关闭}，则有一个顶点$ z $，而不是$ a \ a \ a \ cup b $ a \ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $。 在本文中，我们调查了$ n $ naugientally封闭的线路图。特别是，我们为存在此类图的存在以及用于查找此类图的无限家族的构造提供了必要条件。我们还证明，恰好有两个$ 2 $的平面线图。然后，我们考虑了超图的界限和构造的生存闭合，并以$ 2 $的封闭式封闭的封闭方式图。
A graph $G$ is {\it $n$-existentially closed} if, for all disjoint sets of vertices $A$ and $B$ with $|A\cup B|=n$, there is a vertex $z$ not in $A\cup B$ adjacent to each vertex of $A$ and to no vertex of $B$. In this paper, we investigate $n$-existentially closed line graphs. In particular, we present necessary conditions for the existence of such graphs as well as constructions for finding infinite families of such graphs. We also prove that there are exactly two $2$-existentially closed planar line graphs. We then consider the existential closure of the line graphs of hypergraphs and present constructions for $2$-existentially closed line graphs of hypergraphs.
