1-平面图的书厚是常数
The Book Thickness of 1-Planar Graphs is Constant
摘要：
在书嵌入中，图的顶点被放置在书的书脊上，边被分配给页面，以便同一页面上的边不会交叉。在本文中，我们证明了每一个$1$ -平面图（即，一个图，可以画在平面上，使没有边是交叉超过一次）允许一个嵌入在一本书与常数页数。据我们所知，最好的非平凡先前上界是$O(\sqrt{n})$，其中$n$是图的顶点数。
英文摘要：
In a book embedding, the vertices of a graph are placed on the spine of a book and the edges are assigned to pages, so that edges on the same page do not cross. In this paper, we prove that every $1$-planar graph (that is, a graph that can be drawn on the plane such that no edge is crossed more than once) admits an embedding in a book with constant number of pages. To the best of our knowledge, the best non-trivial previous upper-bound is $O(\sqrt{n})$, where $n$ is the number of vertices of the graph.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
