论文标题
关于本地有限图的子图类的注释
A note on classes of subgraphs of locally finite graphs
论文作者
论文摘要
我们研究了一个问题，如果图将其包含给定类别的局部有限图的所有成员作为子图或诱导的子图。更确切地说，我们为存在连接的，有限的图形$ h $的存在提供了必要的条件，其中包含$ \ MATHCAL G $的所有元素。这些条件表明，该类$ h $的类$ \ Mathcal g_d $由所有图表组成，所有图表$ <d $ $ <d $，这引发了一个问题，在这种情况下，是否可以选择$ h $的最高度。我们表明事实并非如此，从而回答了Huynh等人最近提出的一个问题。
We investigate the question how `small' a graph can be, if it contains all members of a given class of locally finite graphs as subgraphs or induced subgraphs. More precisely, we give necessary and sufficient conditions for the existence of a connected, locally finite graph $H$ containing all elements of a graph class $\mathcal G$. These conditions imply that such a graph $H$ exists for the class $\mathcal G_d$ consisting of all graphs with maximum degree $<d$ which raises the question whether in this case $H$ can be chosen to have bounded maximum degree. We show that this is not the case, thereby answering a question recently posed by Huynh et al.
