Andrea C. Burgess, Robert D. Luther, David A. Pike
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引用次数: 0
Abstract
A graph is 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 five 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.
如果对于所有具有 \(|A\cup B|=n\) 的顶点集 A 和 B，有一个不在\(A/cup B\) 中的顶点 z 与 A 的每个顶点相邻，并且与 B 的任何顶点都不相邻，那么这个图就是 n-existentially closed。特别是，我们提出了这种图存在的必要条件，以及找到这种图无限族的构造。我们还证明了正好有五个 2-existent closed 平面线图。然后，我们考虑了超图的线图的存在封闭性，并提出了 2-existentially closed line graphs of hypergraphs 的构造。
期刊介绍：
Graphs and Combinatorics is an international journal devoted to research concerning all aspects of combinatorial mathematics. In addition to original research papers, the journal also features survey articles from authors invited by the editorial board.
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