论文标题
完整多部分图的家庭尺寸
Family sizes for complete multipartite graphs
论文作者
论文摘要
尚不清楚用无结嵌入的图形设置的障碍物，但是最近的戈德堡，马特曼和奈米的一篇论文表明它很大。几乎所有已知的障碍物都属于四个三角形的家庭，他们询问是否有一种有效的方法来查找或估计此类图家庭的大小。受这个问题的启发，我们研究了完整多部分图的家庭规模。除了三个似乎成倍增长的家庭外，这些家庭还稳定了：在某个点之后，增加固定零件中的顶点的数量不会改变家庭规模。
The obstruction set for graphs with knotless embeddings is not known, but a recent paper of Goldberg, Mattman, and Naimi indicates that it is quite large. Almost all known obstructions fall into four Triangle-Y families and they ask if there is an efficient way of finding or estimating the size of such graph families. Inspired by this question, we investigate the family size for complete multipartite graphs. Aside from three families that appear to grow exponentially, these families stabilize: after a certain point, increasing the number of vertices in a fixed part does not change family size.
