通过分层分隔符实现堆栈和队列布局
Stack and Queue Layouts via Layered Separators
摘要：
已知图的每一个真次闭类都有有界栈数（又称栈数）。书的厚度和页码）。虽然这包括著名的图族，如平面图和有界亏格的图，但许多其他图族在取子式下并不封闭。对于固定的$g$和$k$，我们表明，每一个$n$顶点图，可以嵌入在表面上的属$g$与最多$k$交叉每边有堆叠数$\mathcal{O}(\log n)$，这包括$k$ -平面图。除了$1$ -平面图的情况外，这些族的栈数的以前最著名的界是$\mathcal{O}(\sqrt{n})$。对于可嵌入到固定亏格曲面上的映射图，证明了类似的结果。这些家庭没有一个因收养未成年人而被关闭。在证明这些结果的主要成分是一个构造证明$n$ -顶点图，允许常数分层分离符有$\mathcal{O}(\log n)$栈数。
英文摘要：
It is known that every proper minor-closed class of graphs has bounded stack-number (a.k.a. book thickness and page number). While this includes notable graph families such as planar graphs and graphs of bounded genus, many other graph families are not closed under taking minors. For fixed $g$ and $k$, we show that every $n$-vertex graph that can be embedded on a surface of genus $g$ with at most $k$ crossings per edge has stack-number $\mathcal{O}(\log n)$; this includes $k$-planar graphs. The previously best known bound for the stack-number of these families was $\mathcal{O}(\sqrt{n})$, except in the case of $1$-planar graphs. Analogous results are proved for map graphs that can be embedded on a surface of fixed genus. None of these families is closed under taking minors. The main ingredient in the proof of these results is a construction proving that $n$-vertex graphs that admit constant layered separators have $\mathcal{O}(\log n)$ stack-number.
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