论文标题
在具有最大开放包装的图表上
On graphs having one size of maximal open packings
论文作者
论文摘要
如果$ g $的$ g $中的$ p $顶点是一个开放包装，如果$ p $中没有两个不同的顶点，则具有共同的邻居。在$ g $中的所有最大开放包装中，最小的基数表示为$ρ^{\ rm o} _l（g）$，最大的基数为$ρ^{\ rm o}（g）$。存在这两个不变性的图表。在本文中，我们开始研究具有最大开放包装大小的图形类别。通过介绍一种构造此类图的方法，我们表明每个图是此类中图的诱导子图。本文的主要结果是那些没有订单周期小于$ 15 $的$ g $的结构表征，$ρ^{\ rm o} _l（g）=ρ^{\ rm o}（g）$。
A set $P$ of vertices in a graph $G$ is an open packing if no two distinct vertices in $P$ have a common neighbor. Among all maximal open packings in $G$, the smallest cardinality is denoted $ρ^{\rm o}_L(G)$ and the largest cardinality is $ρ^{\rm o}(G)$. There exist graphs for which these two invariants are arbitrarily far apart. In this paper we begin the investigation of the class of graphs that have one size of maximal open packings. By presenting a method of constructing such graphs we show that every graph is the induced subgraph of a graph in this class. The main result of the paper is a structural characterization of those $G$ that do not have a cycle of order less than $15$ and for which $ρ^{\rm o}_L(G)=ρ^{\rm o}(G)$.
