论文标题
拓扑次要关系的通用平面图
Universal planar graphs for the topological minor relation
论文作者
论文摘要
Huynh等。最近表明，一个可数的图形$ g $包含每个可数平面图作为子图，必须包含任意较大的有限完整图作为拓扑未成年人，而无限完整的图作为辅修图。如果$ g $包含每个可数的平面图作为拓扑辅助，我们可以通过表明相同的结论来加强这一结果。特别是，没有可计数的平面图，其中包含每个可数平面图作为拓扑辅修图，回答了Diestel和Kühn的问题。 此外，我们构建了一个本地有限的平面图，该图包含每个本地有限的平面图作为拓扑辅修图。这表明在上述结果中，不足以要求$ g $包含每个本地有限的平面图作为拓扑辅助图。
Huynh et al. recently showed that a countable graph $G$ which contains every countable planar graph as a subgraph must contain arbitrarily large finite complete graphs as topological minors, and an infinite complete graph as a minor. We strengthen this result by showing that the same conclusion holds, if $G$ contains every countable planar graph as a topological minor. In particular, there is no countable planar graph containing every countable planar graph as a topological minor, answering a question by Diestel and Kühn. Moreover, we construct a locally finite planar graph which contains every locally finite planar graph as a topological minor. This shows that in the above result it is not enough to require that $G$ contains every locally finite planar graph as a topological minor.
