论文标题
拓扑次要关系的通用图
Universal graphs for the topological minor relation
论文作者
论文摘要
一个子图形图/拓扑次要的言语图形$ \ Mathcal {g} $是$ \ Mathcal {G} $中的图形，它包含$ \ Mathcal {G} $中的每个图作为子级别/拓扑辅助的辅助/拓扑。我们证明所有可数平面图的类$ \ Mathcal {p} $不包含拓扑次要的宇宙图。这回答了Diestel和Kühn的问题，并加强了Pach的结果，指出$ \ Mathcal {p} $中没有子图形图。此外，我们表征了哪个细分星$ t $在所有可数$ t $ free图的类别中都有一个拓扑次要的言语图。
A subgraph-universal graph/a topological minor-universal graph in a class of graphs $\mathcal{G}$ is a graph in $\mathcal{G}$ which contains every graph in $\mathcal{G}$ as a subgraph/topological minor. We prove that the class $\mathcal{P}$ of all countable planar graphs does not contain a topological minor-universal graph. This answers a question of Diestel and Kühn and strengthens a result of Pach stating that there is no subgraph-universal graph in $\mathcal{P}$. Furthermore, we characterise for which subdivided stars $T$ there is a topological minor-universal graph in the class of all countable $T$-free graphs.
