图积的书嵌入
Book Embeddings of Graph Products
摘要：
图的$k$ -栈布局（也称为$k$ -页书嵌入）由顶点的全序和相对于顶点序将边划分为非交叉边的$k$集合组成。图的堆叠数（书厚、页码）是允许$k$堆叠布局的最小$k$。类似地定义$k$队列布局，不同之处在于不能嵌套单个集合中的两个边。最近证明了各种非次闭类的图都是路与有界树宽图的强积的子图。受此分解结果的启发，我们探索了图产品的堆栈布局。我们证明了路与（i）有界路宽图或（ii）有界树宽和有界度的二部图的强积的栈数是有界的。结果是通过一个新的概念，同时堆栈队列布局，这可能是独立的利益。
英文摘要：
A $k$-stack layout (also called a $k$-page book embedding) of a graph consists of a total order of the vertices, and a partition of the edges into $k$ sets of non-crossing edges with respect to the vertex order. The stack number (book thickness, page number) of a graph is the minimum $k$ such that it admits a $k$-stack layout. A $k$-queue layout is defined similarly, except that no two edges in a single set may be nested. It was recently proved that graphs of various non-minor-closed classes are subgraphs of the strong product of a path and a graph with bounded treewidth. Motivated by this decomposition result, we explore stack layouts of graph products. We show that the stack number is bounded for the strong product of a path and (i) a graph of bounded pathwidth or (ii) a bipartite graph of bounded treewidth and bounded degree. The results are obtained via a novel concept of simultaneous stack-queue layouts, which may be of independent interest.
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。
