论文标题
统一的$ 3 $连接图的属性
Properties of uniformly $3$-connected graphs
论文作者
论文摘要
如果每对顶点通过$ k $连接而不超过$ k $独立路径，则至少$ {k+1} $ vertices均均匀地连接了$ k $。我们重新研究了均匀$ 3 $连接的图表的最新建设性表征，并获得了更详细的结果，将顶点数与构造相应均匀$ 3 $连接的图的操作相关联。此外，我们研究了在上述结构下如何跨越数字和树宽。我们演示了如何利用这些结果来研究均匀的3 $连接图的结构和特性，最低数量的顶点数量最少。
A graph on at least ${k+1}$ vertices is uniformly $k$-connected if each pair of its vertices is connected by $k$ and not more than $k$ independent paths. We reinvestigate a recent constructive characterization of uniformly $3$-connected graphs and obtain a more detailed result that relates the number of vertices to the operations involved in constructing a respective uniformly $3$-connected graph. Furthermore, we investigate how crossing numbers and treewidths behave under the mentioned constructions. We demonstrate how these results can be utilized to study the structure and properties of uniformly $3$-connected graphs with minimum number of vertices of minimum degree.
