论文标题
在带有次要元素的图表上
On graph classes with minor-universal elements
论文作者
论文摘要
图形$ u $对于图类类$ \ MATHCAL {C} \ ni U $是通用的，如果每个$ g \ in \ Mathcal {C} $都是$ u $的少数。我们证明了几个自然图类中的通用图的存在或不存在，包括可嵌入表面的图形组件，以及禁止$ k_5 $的图形，或$ k_ {3,3,3} $，或$ k_ \ iffty $作为未成年人。我们证明了（do and）没有通用元素的许多次要次数可计数图的存在。 我们的某些结果和问题可能引起了有限图理论家的关注。特别是，我们的侧重点之一是，每个$ k_5 $ - 毫米的图形都是$ k_5 $ - 最高度22的$ k_5 $ fime-minor图。
A graph $U$ is universal for a graph class $\mathcal{C}\ni U$, if every $G\in \mathcal{C}$ is a minor of $U$. We prove the existence or absence of universal graphs in several natural graph classes, including graphs component-wise embeddable into a surface, and graphs forbidding $K_5$, or $K_{3,3}$, or $K_\infty$ as a minor. We prove the existence of uncountably many minor-closed classes of countable graphs that (do and) do not have a universal element. Some of our results and questions may be of interest to the finite graph theorist. In particular, one of our side-results is that every $K_5$-minor-free graph is a minor of a $K_5$-minor-free graph of maximum degree 22.
